Discrete feedback control was designed to stabilize an unstable hybrid neutral stochastic differential delay system(HNSDDS) under a highly nonlinear constraint in the H_∞ and exponential forms.Nevertheless,the existi...Discrete feedback control was designed to stabilize an unstable hybrid neutral stochastic differential delay system(HNSDDS) under a highly nonlinear constraint in the H_∞ and exponential forms.Nevertheless,the existing work just adapted to autonomous cases,and the obtained results were mainly on exponential stabilization.In comparison with autonomous cases,non-autonomous systems are of great interest and represent an important challenge.Accordingly,discrete feedback control has here been adjusted with a time factor to stabilize an unstable non-autonomous HNSDDS,in which new Lyapunov-Krasovskii functionals and some novel technologies are adopted.It should be noted,in particular,that the stabilization can be achieved not only in the routine H_∞ and exponential forms,but also the polynomial form and even a general form.展开更多
The robust stability and robust stabilization problems for discrete singular systems with interval time-varying delay and linear fractional uncertainty are discussed. A new delay-dependent criterion is established for...The robust stability and robust stabilization problems for discrete singular systems with interval time-varying delay and linear fractional uncertainty are discussed. A new delay-dependent criterion is established for the nominal discrete singular delay systems to be regular, causal and stable by employing the linear matrix inequality (LMI) approach. It is shown that the newly proposed criterion can provide less conservative results than some existing ones. Then, with this criterion, the problems of robust stability and robust stabilization for uncertain discrete singular delay systems are solved, and the delay-dependent LMI conditions are obtained. Finally, numerical examples are given to illustrate the effectiveness of the proposed approach.展开更多
In this paper, the problem of stability analysis of discrete-time delay systems with two additive time-varying delays is considered. A new stability result is derived for a general class of delay systems which has pra...In this paper, the problem of stability analysis of discrete-time delay systems with two additive time-varying delays is considered. A new stability result is derived for a general class of delay systems which has practical application background in networked control systems . The stability criterion is expressed in the form of linear matrix inequalities (LMIs), which can be readily solved by using standard numerical software. An illustrative example is provided to show the advantage of the proposed stability condition.展开更多
The robust stability of uncertain linear degenerate systems with discrete and distributed delays is studied in this paper. The uncertainties under consideration are norm bounded, and possibly time varying. A novel rob...The robust stability of uncertain linear degenerate systems with discrete and distributed delays is studied in this paper. The uncertainties under consideration are norm bounded, and possibly time varying. A novel robust stability criterion of the system is derived by constructing Lyapunov functions. The degenerate systems are transformed to a descriptor system and the stability criteria are formulated in the form of a linear matrix inequality (LMI). Therefore, it is easy to check the robust stability of the degenerate systems by using this method. Numerical examples are also worked out to illustrate the obtained results.展开更多
A discrete predictor-based control method is developed for a class of linear time-invariant networked control systems with a sensor-to-controller time-varying delay and a controller-to-actuator uncertain constant dela...A discrete predictor-based control method is developed for a class of linear time-invariant networked control systems with a sensor-to-controller time-varying delay and a controller-to-actuator uncertain constant delay,which can be potentially applied to vision-based control systems.The control scheme is composed of a state prediction and a discrete predictor-based controller.The state prediction is used to compensate for the effect of the sensor-to-controller delay,and the system can be stabilized by the discrete predictor-based controller.Moreover,it is shown that the control scheme is also robust with respect to slight message rejections.Finally,the main theoretical results are illustrated by simulation results and experimental results based on a networked visual servo inverted pendulum system.展开更多
A discrete variable structure control(DVSC) method for the linear time invariant systems with time delay was presented. The continuous time delay systems are first transformed into the standard discrete form which con...A discrete variable structure control(DVSC) method for the linear time invariant systems with time delay was presented. The continuous time delay systems are first transformed into the standard discrete form which contains no time delay by augmenting the state variables. Then the switching surface is determined by using the ideal quasi sliding mode. As it is difficult for the state trajectory to reach the switching surface exactly, the reaching condition in the form of approach law is used to design the controller. The deduced switching surface and controller contain not only the current step of state feedback but also some former steps of controls. Stability analysis with and without time delay information is also investigated in this paper. Numerical simulation was carried out to demonstrate the effectiveness and feasibility of the presented control method.展开更多
Stochastic switched epidemic systems with a discrete or distributed time delay are constructed and investigated. By the Lyapunov method and lto's differential rule, the existence and uniqueness of global positive sol...Stochastic switched epidemic systems with a discrete or distributed time delay are constructed and investigated. By the Lyapunov method and lto's differential rule, the existence and uniqueness of global positive solution of each system is proved. And stability conditions of the disease-free equilibrium of the systems are obtained. Numerical simulations are presented to illustrate the results.展开更多
A delayed Lotka-Volterra two-species predator-prey system of population allelopathy with discrete delay is considered. By linearizing the system at the positive equilibrium and analyzing the associated characteristic ...A delayed Lotka-Volterra two-species predator-prey system of population allelopathy with discrete delay is considered. By linearizing the system at the positive equilibrium and analyzing the associated characteristic equation, the asymptotic stability of the positive equilibrium is investigated and Hopf bifurcations are demonstrated. Furthermore, the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are determined by the normal form theory and the center manifold theorem for functional differential equations (FDEs). Finally, some numerical simulations are carried out for illustrating the theoretical results.展开更多
This paper considers the problem of robust passive control for uncertain discrete systems with time-varying delays. We pay attention to designing a state feedback controller which guarantees the passivity of the close...This paper considers the problem of robust passive control for uncertain discrete systems with time-varying delays. We pay attention to designing a state feedback controller which guarantees the passivity of the closed-loop system for all admissible uncertainties. In terms of a linear matrix inequality, a sufficient condition for the solvability of this problem is presented and the explicit expression of the desired state feedback controller is given.展开更多
This paper considers the problem of delay-dependent robust optimal H<sub>∞</sub> control for a class of uncertain two-dimensional (2-D) discrete state delay systems described by the general model (GM). Th...This paper considers the problem of delay-dependent robust optimal H<sub>∞</sub> control for a class of uncertain two-dimensional (2-D) discrete state delay systems described by the general model (GM). The parameter uncertainties are assumed to be norm-bounded. A linear matrix inequality (LMI)-based sufficient condition for the existence of delay-dependent g-suboptimal state feedback robust H<sub>∞</sub> controllers which guarantees not only the asymptotic stability of the closed-loop system, but also the H<sub>∞</sub> noise attenuation g over all admissible parameter uncertainties is established. Furthermore, a convex optimization problem is formulated to design a delay-dependent state feedback robust optimal H<sub>∞</sub> controller which minimizes the H<sub>∞</sub> noise attenuation g of the closed-loop system. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed method.展开更多
In this paper, global input-to-state stability (ISS) for discrete-time piecewise affine systems with time-delay are considered Piecewise quadratic ISS-Lyapunov functions are adopted. Both Lyapunov-Razumikhiu and Lya...In this paper, global input-to-state stability (ISS) for discrete-time piecewise affine systems with time-delay are considered Piecewise quadratic ISS-Lyapunov functions are adopted. Both Lyapunov-Razumikhiu and Lyapunov-Krasovskii methods are used The theorems of Lyapunov-Razumikhin type and Lyapunov-Krasovskii type for piecewise affine systems with time-delay are shown respectively.展开更多
The dynamics of discrete time delayed Hopfield neural networks is investigated. By using a difference inequality combining with the linear matrix inequality, a sufficient condition ensuring global exponential stabilit...The dynamics of discrete time delayed Hopfield neural networks is investigated. By using a difference inequality combining with the linear matrix inequality, a sufficient condition ensuring global exponential stability of the unique equilibrium point of the networks is found. The result obtained holds not only for constant delay but also for time-varying delays.展开更多
The input time delay is always existent in the practical systems. Analysis of the delay phenomenon in a continuous-time domain is sophisticated. It is appropriate to obtain its corresponding discrete-time model for im...The input time delay is always existent in the practical systems. Analysis of the delay phenomenon in a continuous-time domain is sophisticated. It is appropriate to obtain its corresponding discrete-time model for implementation via digital computer. This paper proposes a new discretization method for calculating a sampled-data representation of nonlinear time-delayed non-affine systems. The proposed scheme provides a finite-dimensional representation for nonlinear systems with non-a^ne time-delayed input enabling existing nonlinear controller design techniques to be applied to them. The performance of the proposed discretization procedure is evaluated by using a nonlinear system with non-affine time-delayed input. For this nonlinear system, various time delay values are considered.展开更多
Discrete Hopfield neural network with delay is an extension of discrete Hopfield neural network. As it is well known, the stability of neural networks is not only the most basic and important problem but also foundati...Discrete Hopfield neural network with delay is an extension of discrete Hopfield neural network. As it is well known, the stability of neural networks is not only the most basic and important problem but also foundation of the network's applications. The stability of discrete HJopfield neural networks with delay is mainly investigated by using Lyapunov function. The sufficient conditions for the networks with delay converging towards a limit cycle of length 4 are obtained. Also, some sufficient criteria are given to ensure the networks having neither a stable state nor a limit cycle with length 2. The obtained results here generalize the previous results on stability of discrete Hopfield neural network with delay and without delay.展开更多
A general model of linearly stochastically coupled identical connected neural networks with hybrid coupling is proposed, which is composed of constant coupling, coupling discrete time-varying delay and coupling distri...A general model of linearly stochastically coupled identical connected neural networks with hybrid coupling is proposed, which is composed of constant coupling, coupling discrete time-varying delay and coupling distributed timevarying delay. All the coupling terms are subjected to stochastic disturbances described in terms of Brownian motion, which reflects a more realistic dynamical behaviour of coupled systems in practice. Based on a simple adaptive feedback controller and stochastic stability theory, several sufficient criteria are presented to ensure the synchronization of linearly stochastically coupled complex networks with coupling mixed time-varying delays. Finally, numerical simulations illustrated by scale-free complex networks verify the effectiveness of the proposed controllers.展开更多
In this paper, we construct a backward difference scheme for a class of SIR epidemic model with general incidence f . The step sizeτ used in our discretization is one. The dynamical properties are investigated (posit...In this paper, we construct a backward difference scheme for a class of SIR epidemic model with general incidence f . The step sizeτ used in our discretization is one. The dynamical properties are investigated (positivity and the boundedness of solution). By constructing the Lyapunov function, the general incidence function f must satisfy certain assumptions, under which, we establish the global stability of endemic equilibrium when R0 >1. The global stability of diseases-free equilibrium is also established when R0 ≤1. In addition we present numerical results of the continuous and discrete model of the different class according to the value of basic reproduction number R0.展开更多
Due to the gathering of sickrooms and consultation rooms in almost all hospitals, the performance of wireless devices system is deteriorated by the increase of collision probability and waiting time. In order to impro...Due to the gathering of sickrooms and consultation rooms in almost all hospitals, the performance of wireless devices system is deteriorated by the increase of collision probability and waiting time. In order to improve the performance of wireless devices system, relay is added to control the access point and then the access of devices is distributed. The concentration of access point is avoided and then the performance of system is expected to be improved. The discrete time Markov chain (DTMC) is proposed to calculate the access probability of devices in a duration time slot. The collision probability, throughput, delay, bandwidth and so on are theoretically calculated based on the standard IEEE802.15.6 and the performance of the system with and without relay is compared. The numerical result indicates that the performance of the system with control access point is higher than that of the system without control access point when the number of devices and/or packet arrive rate are high. However, the system with control access point is more complicated. It is the trade-off between the performance and the complication.展开更多
A class of non-autonomous two species Lotka-Volterra competitive system with pure discrete time delays is discussed. Some sufficient conditions on the boundedness, permanence, periodic solution and global attractivity...A class of non-autonomous two species Lotka-Volterra competitive system with pure discrete time delays is discussed. Some sufficient conditions on the boundedness, permanence, periodic solution and global attractivity of the system are established by means of the comparison method and Liapunov functional.展开更多
This paper focuses on the robust control issue for interval type-2 Takagi-Sugeno(IT2 T-S)fuzzy discrete systems with input delays and cyber attacks.The lower and upper membership functions are first utilized to IT2 fu...This paper focuses on the robust control issue for interval type-2 Takagi-Sugeno(IT2 T-S)fuzzy discrete systems with input delays and cyber attacks.The lower and upper membership functions are first utilized to IT2 fuzzy discrete systems to capture parameter uncertainties.By considering the influences of input delays and stochastic cyber attacks,a newly fuzzy robust controller is established.Afterward,the asymptotic stability sufficient conditions in form of LMIs for the IT2 closed-loop systems are given via establishing a Lyapunov-Krasovskii functional.Afterward,a solving algorithm for obtaining the controller gains is given.Finally,the effectiveness of the developed IT2 fuzzy method is verified by a numerical example.展开更多
Active control of a flexible cantilever plate with multiple time delays is investigated using the discrete optimal control method. A controller with multiple time delays is presented. In this controller, time delay ef...Active control of a flexible cantilever plate with multiple time delays is investigated using the discrete optimal control method. A controller with multiple time delays is presented. In this controller, time delay effect is incorporated in the mathematical model of the dynamic system throughout the control design and no approximations and assumptions are made in the controller derivation, so the system stability is easily guaranteed. Furthermore, this controller is available for both small time delays and large time delays. The feasibility and efficiency of the proposed controller are verified through numerical simulations in the end of this paper.展开更多
基金supported by the National Natural Science Foundation of China(61833005)the Humanities and Social Science Fund of Ministry of Education of China(23YJAZH031)+1 种基金the Natural Science Foundation of Hebei Province of China(A2023209002,A2019209005)the Tangshan Science and Technology Bureau Program of Hebei Province of China(19130222g)。
文摘Discrete feedback control was designed to stabilize an unstable hybrid neutral stochastic differential delay system(HNSDDS) under a highly nonlinear constraint in the H_∞ and exponential forms.Nevertheless,the existing work just adapted to autonomous cases,and the obtained results were mainly on exponential stabilization.In comparison with autonomous cases,non-autonomous systems are of great interest and represent an important challenge.Accordingly,discrete feedback control has here been adjusted with a time factor to stabilize an unstable non-autonomous HNSDDS,in which new Lyapunov-Krasovskii functionals and some novel technologies are adopted.It should be noted,in particular,that the stabilization can be achieved not only in the routine H_∞ and exponential forms,but also the polynomial form and even a general form.
基金supported by Research Foundation of Education Bureau of Shannxi Province, PRC(No.2010JK400)
文摘The robust stability and robust stabilization problems for discrete singular systems with interval time-varying delay and linear fractional uncertainty are discussed. A new delay-dependent criterion is established for the nominal discrete singular delay systems to be regular, causal and stable by employing the linear matrix inequality (LMI) approach. It is shown that the newly proposed criterion can provide less conservative results than some existing ones. Then, with this criterion, the problems of robust stability and robust stabilization for uncertain discrete singular delay systems are solved, and the delay-dependent LMI conditions are obtained. Finally, numerical examples are given to illustrate the effectiveness of the proposed approach.
基金supported by Shanghai Leading Academic Discipline Project (No.B540)
文摘In this paper, the problem of stability analysis of discrete-time delay systems with two additive time-varying delays is considered. A new stability result is derived for a general class of delay systems which has practical application background in networked control systems . The stability criterion is expressed in the form of linear matrix inequalities (LMIs), which can be readily solved by using standard numerical software. An illustrative example is provided to show the advantage of the proposed stability condition.
文摘The robust stability of uncertain linear degenerate systems with discrete and distributed delays is studied in this paper. The uncertainties under consideration are norm bounded, and possibly time varying. A novel robust stability criterion of the system is derived by constructing Lyapunov functions. The degenerate systems are transformed to a descriptor system and the stability criteria are formulated in the form of a linear matrix inequality (LMI). Therefore, it is easy to check the robust stability of the degenerate systems by using this method. Numerical examples are also worked out to illustrate the obtained results.
基金supported by the China Scholarship Council(CSC)the National Natural Science Foundation of China(92067106)。
文摘A discrete predictor-based control method is developed for a class of linear time-invariant networked control systems with a sensor-to-controller time-varying delay and a controller-to-actuator uncertain constant delay,which can be potentially applied to vision-based control systems.The control scheme is composed of a state prediction and a discrete predictor-based controller.The state prediction is used to compensate for the effect of the sensor-to-controller delay,and the system can be stabilized by the discrete predictor-based controller.Moreover,it is shown that the control scheme is also robust with respect to slight message rejections.Finally,the main theoretical results are illustrated by simulation results and experimental results based on a networked visual servo inverted pendulum system.
文摘A discrete variable structure control(DVSC) method for the linear time invariant systems with time delay was presented. The continuous time delay systems are first transformed into the standard discrete form which contains no time delay by augmenting the state variables. Then the switching surface is determined by using the ideal quasi sliding mode. As it is difficult for the state trajectory to reach the switching surface exactly, the reaching condition in the form of approach law is used to design the controller. The deduced switching surface and controller contain not only the current step of state feedback but also some former steps of controls. Stability analysis with and without time delay information is also investigated in this paper. Numerical simulation was carried out to demonstrate the effectiveness and feasibility of the presented control method.
基金supported by the National Natural Science Foundation of China(60874114)
文摘Stochastic switched epidemic systems with a discrete or distributed time delay are constructed and investigated. By the Lyapunov method and lto's differential rule, the existence and uniqueness of global positive solution of each system is proved. And stability conditions of the disease-free equilibrium of the systems are obtained. Numerical simulations are presented to illustrate the results.
文摘A delayed Lotka-Volterra two-species predator-prey system of population allelopathy with discrete delay is considered. By linearizing the system at the positive equilibrium and analyzing the associated characteristic equation, the asymptotic stability of the positive equilibrium is investigated and Hopf bifurcations are demonstrated. Furthermore, the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are determined by the normal form theory and the center manifold theorem for functional differential equations (FDEs). Finally, some numerical simulations are carried out for illustrating the theoretical results.
文摘This paper considers the problem of robust passive control for uncertain discrete systems with time-varying delays. We pay attention to designing a state feedback controller which guarantees the passivity of the closed-loop system for all admissible uncertainties. In terms of a linear matrix inequality, a sufficient condition for the solvability of this problem is presented and the explicit expression of the desired state feedback controller is given.
文摘This paper considers the problem of delay-dependent robust optimal H<sub>∞</sub> control for a class of uncertain two-dimensional (2-D) discrete state delay systems described by the general model (GM). The parameter uncertainties are assumed to be norm-bounded. A linear matrix inequality (LMI)-based sufficient condition for the existence of delay-dependent g-suboptimal state feedback robust H<sub>∞</sub> controllers which guarantees not only the asymptotic stability of the closed-loop system, but also the H<sub>∞</sub> noise attenuation g over all admissible parameter uncertainties is established. Furthermore, a convex optimization problem is formulated to design a delay-dependent state feedback robust optimal H<sub>∞</sub> controller which minimizes the H<sub>∞</sub> noise attenuation g of the closed-loop system. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed method.
基金supported by National Natural Science Foundation of China (No. 60874006)Natural Science Foundation of Hei-longjiang Province for Youth (No. QC2009C99)
文摘In this paper, global input-to-state stability (ISS) for discrete-time piecewise affine systems with time-delay are considered Piecewise quadratic ISS-Lyapunov functions are adopted. Both Lyapunov-Razumikhiu and Lyapunov-Krasovskii methods are used The theorems of Lyapunov-Razumikhin type and Lyapunov-Krasovskii type for piecewise affine systems with time-delay are shown respectively.
基金Project supported by the Program for New Century Excellent Talents in University (Grant No NCET-06-0298)the Program for Liaoning Excellent Talents in University (Grant No RC-05-07)+1 种基金the Program for Study of Science of the Educational Department of Liaoning Province, China (Grant No 05L020)the Program for Dalian Science and Technology of China (Grant No2005A10GX106)
文摘The dynamics of discrete time delayed Hopfield neural networks is investigated. By using a difference inequality combining with the linear matrix inequality, a sufficient condition ensuring global exponential stability of the unique equilibrium point of the networks is found. The result obtained holds not only for constant delay but also for time-varying delays.
基金supported by University Natural Science Research Project of Jiangsu Province (No. 10KJB510001)
文摘The input time delay is always existent in the practical systems. Analysis of the delay phenomenon in a continuous-time domain is sophisticated. It is appropriate to obtain its corresponding discrete-time model for implementation via digital computer. This paper proposes a new discretization method for calculating a sampled-data representation of nonlinear time-delayed non-affine systems. The proposed scheme provides a finite-dimensional representation for nonlinear systems with non-a^ne time-delayed input enabling existing nonlinear controller design techniques to be applied to them. The performance of the proposed discretization procedure is evaluated by using a nonlinear system with non-affine time-delayed input. For this nonlinear system, various time delay values are considered.
文摘Discrete Hopfield neural network with delay is an extension of discrete Hopfield neural network. As it is well known, the stability of neural networks is not only the most basic and important problem but also foundation of the network's applications. The stability of discrete HJopfield neural networks with delay is mainly investigated by using Lyapunov function. The sufficient conditions for the networks with delay converging towards a limit cycle of length 4 are obtained. Also, some sufficient criteria are given to ensure the networks having neither a stable state nor a limit cycle with length 2. The obtained results here generalize the previous results on stability of discrete Hopfield neural network with delay and without delay.
基金Project supported by the National Natural Science Foundation of China (Grant No 60874113)
文摘A general model of linearly stochastically coupled identical connected neural networks with hybrid coupling is proposed, which is composed of constant coupling, coupling discrete time-varying delay and coupling distributed timevarying delay. All the coupling terms are subjected to stochastic disturbances described in terms of Brownian motion, which reflects a more realistic dynamical behaviour of coupled systems in practice. Based on a simple adaptive feedback controller and stochastic stability theory, several sufficient criteria are presented to ensure the synchronization of linearly stochastically coupled complex networks with coupling mixed time-varying delays. Finally, numerical simulations illustrated by scale-free complex networks verify the effectiveness of the proposed controllers.
文摘In this paper, we construct a backward difference scheme for a class of SIR epidemic model with general incidence f . The step sizeτ used in our discretization is one. The dynamical properties are investigated (positivity and the boundedness of solution). By constructing the Lyapunov function, the general incidence function f must satisfy certain assumptions, under which, we establish the global stability of endemic equilibrium when R0 >1. The global stability of diseases-free equilibrium is also established when R0 ≤1. In addition we present numerical results of the continuous and discrete model of the different class according to the value of basic reproduction number R0.
文摘Due to the gathering of sickrooms and consultation rooms in almost all hospitals, the performance of wireless devices system is deteriorated by the increase of collision probability and waiting time. In order to improve the performance of wireless devices system, relay is added to control the access point and then the access of devices is distributed. The concentration of access point is avoided and then the performance of system is expected to be improved. The discrete time Markov chain (DTMC) is proposed to calculate the access probability of devices in a duration time slot. The collision probability, throughput, delay, bandwidth and so on are theoretically calculated based on the standard IEEE802.15.6 and the performance of the system with and without relay is compared. The numerical result indicates that the performance of the system with control access point is higher than that of the system without control access point when the number of devices and/or packet arrive rate are high. However, the system with control access point is more complicated. It is the trade-off between the performance and the complication.
文摘A class of non-autonomous two species Lotka-Volterra competitive system with pure discrete time delays is discussed. Some sufficient conditions on the boundedness, permanence, periodic solution and global attractivity of the system are established by means of the comparison method and Liapunov functional.
基金This research was supported by the National Natural Science Foundation of China under Grant No.61903167.
文摘This paper focuses on the robust control issue for interval type-2 Takagi-Sugeno(IT2 T-S)fuzzy discrete systems with input delays and cyber attacks.The lower and upper membership functions are first utilized to IT2 fuzzy discrete systems to capture parameter uncertainties.By considering the influences of input delays and stochastic cyber attacks,a newly fuzzy robust controller is established.Afterward,the asymptotic stability sufficient conditions in form of LMIs for the IT2 closed-loop systems are given via establishing a Lyapunov-Krasovskii functional.Afterward,a solving algorithm for obtaining the controller gains is given.Finally,the effectiveness of the developed IT2 fuzzy method is verified by a numerical example.
基金the National Natural Science Foundation of China (Nos. 10772112 and 10472065)the KeyProject of Ministry of Education of China (No. 107043)the Specialized Research Fund for the Doctoral Program ofHigher Education of China (No. 20070248032).
文摘Active control of a flexible cantilever plate with multiple time delays is investigated using the discrete optimal control method. A controller with multiple time delays is presented. In this controller, time delay effect is incorporated in the mathematical model of the dynamic system throughout the control design and no approximations and assumptions are made in the controller derivation, so the system stability is easily guaranteed. Furthermore, this controller is available for both small time delays and large time delays. The feasibility and efficiency of the proposed controller are verified through numerical simulations in the end of this paper.