This paper investigates the stability problem for time-varying delay systems.To obtain a larger delay bound,this paper uses the second-order canonical Bessel-Legendre(BL)inequality.Secondly,using four couples of integ...This paper investigates the stability problem for time-varying delay systems.To obtain a larger delay bound,this paper uses the second-order canonical Bessel-Legendre(BL)inequality.Secondly,using four couples of integral terms in the augmented Lyapunov-Krasovskii function(LKF)to enhance the relationship between integral functionals and other vectors.Furthermore,unlike the construction of the traditional LKF,a novel augmented LKF is constructed with two new delayproduct-type terms,which adds more state information and leads to less conservative results.Finally,two numerical examples are provided to demonstrate the effectiveness and the significant improvement of the proposed stability criteria.展开更多
For discrete-time T-S fuzzy systems, the stability and controller design method are in-vestigated based on parameter-dependent Lyapunov function (PDLF). T-S fuzzy systems di?er fromnon-fuzzy systems with polytopic des...For discrete-time T-S fuzzy systems, the stability and controller design method are in-vestigated based on parameter-dependent Lyapunov function (PDLF). T-S fuzzy systems di?er fromnon-fuzzy systems with polytopic description or multi-model description in that the weighting coef-ficients have respective meanings. They, however, have stability aspect in common. By adopting astability condition for polytopic systems obtained via PDLF, and combining the properties of T-Sfuzzy systems, new results are given in this paper. An example shows that by applying the newresults, the stability conditions that can be distinguished are less conservative.展开更多
The stability of the motion control system is one of the decisive factors of the control quality for Autonomous Underwater Vehicle(AUV).The divergence of control,which the unstable system may be brought about,is fat...The stability of the motion control system is one of the decisive factors of the control quality for Autonomous Underwater Vehicle(AUV).The divergence of control,which the unstable system may be brought about,is fatal to the operation of AUV.The stability analysis of the PD and S-surface speed controllers based on the Lyapunov's direct method is proposed in this paper.After decoupling the six degree-of-freedom(DOF)motions of the AUV,the axial dynamic behavior is discussed and the condition is deduced,in which the parameters selection within stability domain can guarantee the system asymptotically stable.The experimental results in a tank and on the sea have successfully verified the algorithm reliability,which can be served as a good reference for analyzing other AUV nonlinear control systems.展开更多
Helical equilibrium of a thin elastic rod has practical backgrounds, such as DNA, fiber, sub-ocean cable, and oil-well drill string. Kirchhoff's kinetic analogy is an effective approach to the stability analysis of e...Helical equilibrium of a thin elastic rod has practical backgrounds, such as DNA, fiber, sub-ocean cable, and oil-well drill string. Kirchhoff's kinetic analogy is an effective approach to the stability analysis of equilibrium of a thin elastic rod. The main hypotheses of Kirchhoff's theory without the extension of the centerline and the shear deformation of the cross section are not adoptable to real soft materials of biological fibers. In this paper, the dynamic equations of a rod with a circular cross section are established on the basis of the exact Cosserat model by considering the tension and the shear deformations. Euler's angles are applied as the attitude representation of the cross section. The deviation of the normal axis of the cross section from the tangent of the centerline is considered as the result of the shear deformation. Lyapunov's stability of the helical equilibrium is discussed in static category. Euler's critical values of axial force and torque are obtained. Lyapunov's and Euler's stability conditions in the space domain are the necessary conditions of Lyapunov's stability of the helical rod in the time domain.展开更多
In this paper, we investigate the stability of a class of impulsive functional differential equations by using Lyapunov functional and Jensen's inequality. Some new stability theorems are obtained. Examples are given...In this paper, we investigate the stability of a class of impulsive functional differential equations by using Lyapunov functional and Jensen's inequality. Some new stability theorems are obtained. Examples are given to demonstrate the advantage of the obtained results.展开更多
Sufficient condition for stochastic unifrom stability of a neutral stochastic functional differential equation is given, especially, new techniques are developed to cope with the neutral delay case, we obtained the su...Sufficient condition for stochastic unifrom stability of a neutral stochastic functional differential equation is given, especially, new techniques are developed to cope with the neutral delay case, we obtained the sufficient condition for asymptotic stability of neutral stochastic differential delay equations. Due to the new techniques developed in this paper, the results obtained arc very general and useful. The theory developed here gives a unified treatment for various asymptotic estimates e.g. exponential and polynomial bounds.展开更多
In this paper, we present a new sufficient condition for absolute stability of Lure system with two additive time-varying delay components. This criterion is expressed as a set of linear matrix inequalities (LMIs), ...In this paper, we present a new sufficient condition for absolute stability of Lure system with two additive time-varying delay components. This criterion is expressed as a set of linear matrix inequalities (LMIs), which can be readily tested by using standard numerical software. We use this new criterion to stabilize a class of nonlinear time-delay systems. Some numerical examples are given to illustrate the applicability of the results using standard numerical software.展开更多
The stability analysis for nonlinear differentialalgebraic systems is addressed using tools from classical control theory. Sufficient stability conditions relying on matrix inequalities are established via Lyapunov Di...The stability analysis for nonlinear differentialalgebraic systems is addressed using tools from classical control theory. Sufficient stability conditions relying on matrix inequalities are established via Lyapunov Direct Method. In addition, a novel interpretation of differential-algebraic systems as feedback interconnection of a purely differential system and an algebraic system allows reducing the stability analysis to a smallgain-like condition. The study of stability properties for constrained mechanical systems, for a class of Lipschitz differential-algebraic systems and for an academic example is used to illustrate the theory.展开更多
The problems of stability and stabilization for the discrete Takagi-Sugeno(T-S) fuzzy time-delay system are investigated.By constructing a discrete piecewise Lyapunov-Krasovskii function(PLKF) in each maximal over...The problems of stability and stabilization for the discrete Takagi-Sugeno(T-S) fuzzy time-delay system are investigated.By constructing a discrete piecewise Lyapunov-Krasovskii function(PLKF) in each maximal overlapped-rules group(MORG),a new sufficient stability condition for the open-loop discrete T-S fuzzy time-delay system is proposed and proved.Then the systematic design of the fuzzy controller is investigated via the parallel distributed compensation control scheme,and a new stabilization condition for the closed-loop discrete T-S fuzzy time-delay system is proposed.The above two sufficient conditions only require finding common matrices in each MORG.Compared with the common Lyapunov-Krasovskii function(CLKF) approach and the fuzzy Lyapunov-Krasovskii function(FLKF) approach,these proposed sufficient conditions can not only overcome the defect of finding common matrices in the whole feasible region but also largely reduce the number of linear matrix inequalities to be solved.Finally,simulation examples show that the proposed PLKF approach is effective.展开更多
This paper proposes a robust power system stabilizer(PSS)for a steam synchronous generator in Barka II power station.The PSS should be capable of damping small-disturbance oscillations(inherently existing in power sys...This paper proposes a robust power system stabilizer(PSS)for a steam synchronous generator in Barka II power station.The PSS should be capable of damping small-disturbance oscillations(inherently existing in power systems due to e.g.load changes,lines switching...etc.)within a certain settling time for different load conditions.Also,the proposed PSS must have the conventional structure and its parameters must not be violated.To achieve this goal,robust control provides many advantages.The suggested controller is tuned by the Kharitonov’s theorem and uses the standard structure employed in industry.The problem is cast into a nonlinear constrained optimization problem to achieve the desired settling time without violating the practical values of the controller parameters.Performance of the robust PSS is evaluated by several simulations in the presence of system uncertainty due to load changes.展开更多
The stabilization and trajectory tracking problems of autonomous airship's planar motion are studied. By defining novel configuration error and velocity error, the dynamics of error systems are derived. By applying L...The stabilization and trajectory tracking problems of autonomous airship's planar motion are studied. By defining novel configuration error and velocity error, the dynamics of error systems are derived. By applying Lyapunov stability method, the state feedback control laws are designed and the close-loop error systems are proved to be uniformly asymptotically stable by Matrosov theorem. In particular, the controller does not need knowledge on system parameters in the case of set-point stabilization, which makes the controller robust with respect to parameter uncertainty. Numerical simulations illustrate the effectiveness of the controller designed.展开更多
This paper investigates the fixed-time stability theorem and state-feedback controller design for stochastic nonlinear systems.We propose an improved fixed-time Lyapunov theorem with a more rigorous and reasonable pro...This paper investigates the fixed-time stability theorem and state-feedback controller design for stochastic nonlinear systems.We propose an improved fixed-time Lyapunov theorem with a more rigorous and reasonable proof procedure.In particular,an important corollary is obtained,which can give a less conservative upper-bound estimate of the settling time.Based on the backstepping technique and the addition of a power integrator method,a state-feedback controller is skillfully designed for a class of stochastic nonlinear systems.It is proved that the proposed controller can render the closed-loop system fixed-time stable in probability with the help of the proposed fixed-time stability criteria.Finally,the effectiveness of the proposed controller is demonstrated by simulation examples and comparisons.展开更多
In this paper, we improve LaSalle's invariance theorem based on Li's work (Li Yong, Asymptotic stability and ultimate boundedness, Northeast. Math. J., 6(1)(1990), 53-59) by relaxing the restrictions, which ma...In this paper, we improve LaSalle's invariance theorem based on Li's work (Li Yong, Asymptotic stability and ultimate boundedness, Northeast. Math. J., 6(1)(1990), 53-59) by relaxing the restrictions, which make the theorem more easy to apply. In addition, we also improve LaSalle's theorem for stochastic differential equation established by Mao (Mao Xuerong, Stochastic versions of the LaSalle theorem, J. Differential Equations, 153(1999), 175-195).展开更多
基金Supported by National Natural Science Foundation of China (60872046) the Key Discipline Development Program of Beijing Municipal Commission (XK100080537)
基金supported by the National Natural Science Foundation of China(61703153)the Natural Science Foundation of Hunan Province(2018JJ4075)
文摘This paper investigates the stability problem for time-varying delay systems.To obtain a larger delay bound,this paper uses the second-order canonical Bessel-Legendre(BL)inequality.Secondly,using four couples of integral terms in the augmented Lyapunov-Krasovskii function(LKF)to enhance the relationship between integral functionals and other vectors.Furthermore,unlike the construction of the traditional LKF,a novel augmented LKF is constructed with two new delayproduct-type terms,which adds more state information and leads to less conservative results.Finally,two numerical examples are provided to demonstrate the effectiveness and the significant improvement of the proposed stability criteria.
文摘For discrete-time T-S fuzzy systems, the stability and controller design method are in-vestigated based on parameter-dependent Lyapunov function (PDLF). T-S fuzzy systems di?er fromnon-fuzzy systems with polytopic description or multi-model description in that the weighting coef-ficients have respective meanings. They, however, have stability aspect in common. By adopting astability condition for polytopic systems obtained via PDLF, and combining the properties of T-Sfuzzy systems, new results are given in this paper. An example shows that by applying the newresults, the stability conditions that can be distinguished are less conservative.
基金supported by the National High Technology Development Program of China(863Program,Grant No.2008AA092301)the Fundamental Research Foundation of Harbin Engineering University(Grant No.HEUFT08001)the Postdoctoral Science Foundation of China(Grant No.20080440838)
文摘The stability of the motion control system is one of the decisive factors of the control quality for Autonomous Underwater Vehicle(AUV).The divergence of control,which the unstable system may be brought about,is fatal to the operation of AUV.The stability analysis of the PD and S-surface speed controllers based on the Lyapunov's direct method is proposed in this paper.After decoupling the six degree-of-freedom(DOF)motions of the AUV,the axial dynamic behavior is discussed and the condition is deduced,in which the parameters selection within stability domain can guarantee the system asymptotically stable.The experimental results in a tank and on the sea have successfully verified the algorithm reliability,which can be served as a good reference for analyzing other AUV nonlinear control systems.
基金supported by the National Natural Science Fundation of China(No.10972143)
文摘Helical equilibrium of a thin elastic rod has practical backgrounds, such as DNA, fiber, sub-ocean cable, and oil-well drill string. Kirchhoff's kinetic analogy is an effective approach to the stability analysis of equilibrium of a thin elastic rod. The main hypotheses of Kirchhoff's theory without the extension of the centerline and the shear deformation of the cross section are not adoptable to real soft materials of biological fibers. In this paper, the dynamic equations of a rod with a circular cross section are established on the basis of the exact Cosserat model by considering the tension and the shear deformations. Euler's angles are applied as the attitude representation of the cross section. The deviation of the normal axis of the cross section from the tangent of the centerline is considered as the result of the shear deformation. Lyapunov's stability of the helical equilibrium is discussed in static category. Euler's critical values of axial force and torque are obtained. Lyapunov's and Euler's stability conditions in the space domain are the necessary conditions of Lyapunov's stability of the helical rod in the time domain.
基金supported by the National Natural Science Foundation of China (No. 10871063)Scientific Research Fund of Hunan Provincial Education Department (No. 07A038)
文摘In this paper, we investigate the stability of a class of impulsive functional differential equations by using Lyapunov functional and Jensen's inequality. Some new stability theorems are obtained. Examples are given to demonstrate the advantage of the obtained results.
基金Supported by the National Natural Science Founda-tion of China (19531070) and the Major Project Foundation of HubeiProvince Education Department (2004Z001)
文摘Sufficient condition for stochastic unifrom stability of a neutral stochastic functional differential equation is given, especially, new techniques are developed to cope with the neutral delay case, we obtained the sufficient condition for asymptotic stability of neutral stochastic differential delay equations. Due to the new techniques developed in this paper, the results obtained arc very general and useful. The theory developed here gives a unified treatment for various asymptotic estimates e.g. exponential and polynomial bounds.
文摘In this paper, we present a new sufficient condition for absolute stability of Lure system with two additive time-varying delay components. This criterion is expressed as a set of linear matrix inequalities (LMIs), which can be readily tested by using standard numerical software. We use this new criterion to stabilize a class of nonlinear time-delay systems. Some numerical examples are given to illustrate the applicability of the results using standard numerical software.
文摘The stability analysis for nonlinear differentialalgebraic systems is addressed using tools from classical control theory. Sufficient stability conditions relying on matrix inequalities are established via Lyapunov Direct Method. In addition, a novel interpretation of differential-algebraic systems as feedback interconnection of a purely differential system and an algebraic system allows reducing the stability analysis to a smallgain-like condition. The study of stability properties for constrained mechanical systems, for a class of Lipschitz differential-algebraic systems and for an academic example is used to illustrate the theory.
基金supported in part by the Scientific Research Project of Heilongjiang Province Education Bureau(12541200)
文摘The problems of stability and stabilization for the discrete Takagi-Sugeno(T-S) fuzzy time-delay system are investigated.By constructing a discrete piecewise Lyapunov-Krasovskii function(PLKF) in each maximal overlapped-rules group(MORG),a new sufficient stability condition for the open-loop discrete T-S fuzzy time-delay system is proposed and proved.Then the systematic design of the fuzzy controller is investigated via the parallel distributed compensation control scheme,and a new stabilization condition for the closed-loop discrete T-S fuzzy time-delay system is proposed.The above two sufficient conditions only require finding common matrices in each MORG.Compared with the common Lyapunov-Krasovskii function(CLKF) approach and the fuzzy Lyapunov-Krasovskii function(FLKF) approach,these proposed sufficient conditions can not only overcome the defect of finding common matrices in the whole feasible region but also largely reduce the number of linear matrix inequalities to be solved.Finally,simulation examples show that the proposed PLKF approach is effective.
文摘This paper proposes a robust power system stabilizer(PSS)for a steam synchronous generator in Barka II power station.The PSS should be capable of damping small-disturbance oscillations(inherently existing in power systems due to e.g.load changes,lines switching...etc.)within a certain settling time for different load conditions.Also,the proposed PSS must have the conventional structure and its parameters must not be violated.To achieve this goal,robust control provides many advantages.The suggested controller is tuned by the Kharitonov’s theorem and uses the standard structure employed in industry.The problem is cast into a nonlinear constrained optimization problem to achieve the desired settling time without violating the practical values of the controller parameters.Performance of the robust PSS is evaluated by several simulations in the presence of system uncertainty due to load changes.
文摘The stabilization and trajectory tracking problems of autonomous airship's planar motion are studied. By defining novel configuration error and velocity error, the dynamics of error systems are derived. By applying Lyapunov stability method, the state feedback control laws are designed and the close-loop error systems are proved to be uniformly asymptotically stable by Matrosov theorem. In particular, the controller does not need knowledge on system parameters in the case of set-point stabilization, which makes the controller robust with respect to parameter uncertainty. Numerical simulations illustrate the effectiveness of the controller designed.
基金supported in part by the National Natural Science Foundation of China(62073166,61673215)the Key Laboratory of Jiangsu Province。
文摘This paper investigates the fixed-time stability theorem and state-feedback controller design for stochastic nonlinear systems.We propose an improved fixed-time Lyapunov theorem with a more rigorous and reasonable proof procedure.In particular,an important corollary is obtained,which can give a less conservative upper-bound estimate of the settling time.Based on the backstepping technique and the addition of a power integrator method,a state-feedback controller is skillfully designed for a class of stochastic nonlinear systems.It is proved that the proposed controller can render the closed-loop system fixed-time stable in probability with the help of the proposed fixed-time stability criteria.Finally,the effectiveness of the proposed controller is demonstrated by simulation examples and comparisons.
基金The 985 Project of Jilin University and Graduate Innovation Lab of Jilin University.
文摘In this paper, we improve LaSalle's invariance theorem based on Li's work (Li Yong, Asymptotic stability and ultimate boundedness, Northeast. Math. J., 6(1)(1990), 53-59) by relaxing the restrictions, which make the theorem more easy to apply. In addition, we also improve LaSalle's theorem for stochastic differential equation established by Mao (Mao Xuerong, Stochastic versions of the LaSalle theorem, J. Differential Equations, 153(1999), 175-195).