The stability analysis of Cohen-Grossberg neural networks with multiple delays is given. An approach combining the Lyapunov functional with the linear matrix inequality (LMI) is taken to obtain the sufficient condit...The stability analysis of Cohen-Grossberg neural networks with multiple delays is given. An approach combining the Lyapunov functional with the linear matrix inequality (LMI) is taken to obtain the sufficient conditions for the globally asymptotic stability of equilibrium point. By using the properties of matrix norm, a practical corollary is derived. All results are established without assuming the differentiability and monotonicity of activation functions. The simulation samples have proved the effectiveness of the conclusions.展开更多
New delay-independent and delay-dependent stability criteria for linear systems with multiple time-varying delays are established by using the time-domain method. The results are derived based on a new-type stability ...New delay-independent and delay-dependent stability criteria for linear systems with multiple time-varying delays are established by using the time-domain method. The results are derived based on a new-type stability theorem for general retarded dynamical systems and new analysis techniques developed in the author's previous work. Unlike some results in the literature, all of the established results do not depend on the derivative of time-varying delays. Therefore, they are suitable for the case with very fast time-varying delays. In addition, some remarks are also given to explain the obtained results and to point out the limitations of the previous results in the literature. Keywords Stability - Delay-independent criteria - Delay-dependent criteria - Linear time-delay systems - Multiple time-varying delays This work was supported by NSFC Key-Project (No. 60334010) and Guangdong Province Natural Science Foundation of China (No. 31406).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
The idea of network splitting according to time delay and weight is introduced.Based on the cyber physical systems(CPS),a class of multi-weighted complex transportation networks with multiple delays is modeled.The fin...The idea of network splitting according to time delay and weight is introduced.Based on the cyber physical systems(CPS),a class of multi-weighted complex transportation networks with multiple delays is modeled.The finite-time synchronization of the proposed complex transportation networks model is studied systematically.On the basis of the theory of stability,the technique of adaptive control,aperiodically intermittent control and finite-time control,the aperiodically intermittent adaptive finite-time synchronization controller is designed.The controller designed in this paper is beneficial for understanding the synchronization in multi-weighted complex transportation networks with multiple delays.In addition,the conditions for the existence of finite time synchronization have been discussed in detail.And the specific value of the settling finite time for synchronization is obtained.Moreover,the outer coupling configuration matrices are not required to be irreducible or symmetric.Finally,simulation results of the finite-time synchronization problem are given to illustrate the correctness of the results obtained.展开更多
An optimal control method for seismic-excited building structures with multiple time delays is investigated in this paper. The system state equation with multiple time delays is discretized and transformed into a stan...An optimal control method for seismic-excited building structures with multiple time delays is investigated in this paper. The system state equation with multiple time delays is discretized and transformed into a standard discrete form without any explicit time delay by a particular augmenting for state variables. A time-delay controller is then designed based on this standard equation using the discrete optimal control method. Effectiveness of the proposed controller is demonstrated by numerical simulations. Simulation results indicate that a very small time delay may result in the instability of the control system if it is not compensated in the control design. Time delay may be compensated effectively by the proposed controller, in the mean time, an effective control may be obtained. The proposed controller is valid for both small and large time delays.展开更多
Global exponential stability problems are investigated for cellular neural networks (CNN) with multiple time-varying delays. Several new criteria in linear matrix inequality form or in algebraic form are presented t...Global exponential stability problems are investigated for cellular neural networks (CNN) with multiple time-varying delays. Several new criteria in linear matrix inequality form or in algebraic form are presented to ascertain the uniqueness and global exponential stability of the equilibrium point for CNN with multiple time-varying delays and with constant time delays. The proposed method has the advantage of considering the difference of neuronal excitatory and inhibitory effects, which is also computationally efficient as it can be solved numerically using the recently developed interior-point algorithm or be checked using simple algebraic calculation. In addition, the proposed results generalize and improve upon some previous works. Two numerical examples are used to show the effectiveness of the obtained results.展开更多
By Fourier analysis techniques and Schauder fixed point theorem, we study the existence of periodic solutions for a class of even order differential equations with multiple delays. The result obtained is a generalizat...By Fourier analysis techniques and Schauder fixed point theorem, we study the existence of periodic solutions for a class of even order differential equations with multiple delays. The result obtained is a generalization of the results developed by W. Layton to the case of multiple delays.展开更多
The HIV problem is studied by version of delay mathematical models which consider the apoptosis of uninfected CD4<sup>+</sup> T cells which cultured with infected T cells in big volume. The opportunistic i...The HIV problem is studied by version of delay mathematical models which consider the apoptosis of uninfected CD4<sup>+</sup> T cells which cultured with infected T cells in big volume. The opportunistic infection and the apoptosis of uninfected CD4<sup>+</sup> T cells are caused directly or indirectly by a toxic substance produced from HIV genes. Ubiquitously, the nonlinear incidence rate brings forth the increasing number of infected CD4<sup>+</sup> T cells with introduction of small time delay, and in addition, there also exists a natural time delay factor during the process of virus replication. With state feedback control of time delay, the bifurcating periodical oscillating phenomena is induced via Hopf bifurcation. Mathematically, with the geometrical criterion applied in the stability analysis of delay model, the critical threshold of Hopf bifurcation in multiple delay differential equations which satisfy the transversal condition is derived. By applying reduction dimensional method combined with the center manifold theory, the stability of the bifurcating periodical solution is analyzed by the perturbation near Hopf point.展开更多
In this paper,we analyze the global dynamics of a neoclassical growth system incorporating patch structure and multiple pairs of time-varying delays.First,we derive the global existence,positiveness and boundedness of...In this paper,we analyze the global dynamics of a neoclassical growth system incorporating patch structure and multiple pairs of time-varying delays.First,we derive the global existence,positiveness and boundedness of solutions for the addressed system.Then,by employing some novel differential inequality analyses and the fluctuation lemma,both delay-independent and delay-dependent criteria are established to ensure that all solutions are convergent to a unique positive equilibrium point vector,which does not possess the same components.Our results supplement and improve some existing results.Ultimately,some numerical examples are afforded to prove the effectiveness and feasibility of the theoretical findings.展开更多
A system of delay differential equations is studied which represent a model for four neurons with time delayed connections between the neurons and time delayed feedback from each neuron to itself. The linear stability...A system of delay differential equations is studied which represent a model for four neurons with time delayed connections between the neurons and time delayed feedback from each neuron to itself. The linear stability and bifurcation of the system are studied in a parameter space consisting of the sum of the time delays between the elements and the product of the strengths of the connections between the elements. Meanwhile, the bifurcation set are drawn in the parameter space.展开更多
In this paper,the robust stability issue of switched uncertain multidelay systems resulting from actuator failures is considered.Based on the average dwell time approach,a set of suitable switching signals is designed...In this paper,the robust stability issue of switched uncertain multidelay systems resulting from actuator failures is considered.Based on the average dwell time approach,a set of suitable switching signals is designed by using the total activation time ratio between the stable subsystem and the unstable one.It is first proven that the resulting closed-loop system is robustly exponentially stable for some allowable upper bound of delays if the nominal system with zero delay is exponentially stable under these switching laws.Particularly,the maximal upper bound of delays can be obtained from the linear matrix inequalities.At last,the effectiveness of the proposed method is demonstrated by a simulation example.展开更多
The object of this article is to study the consequences of occurrence both fault in input and multiple time-varying delays simultaneously while designing observer to estimate the states of agents and also unknown nonl...The object of this article is to study the consequences of occurrence both fault in input and multiple time-varying delays simultaneously while designing observer to estimate the states of agents and also unknown nonlinear fault of system.Two delay dependent criteria are established to show the states of observer reach to states of MAS and also states of observer reach to consensus.From two obtained criteria,it can be deduced,by constructing a distributed controller-based observer design,MAS reach to consensus exponentially.Finally,the advantages of the obtained results are shown by solving an illustrative example.展开更多
This paper is concerned with the optimal linear quadratic Gaussian(LQG)control problem for discrete time-varying system with multiplicative noise and multiple state delays.The main contributions are twofolds.First,in ...This paper is concerned with the optimal linear quadratic Gaussian(LQG)control problem for discrete time-varying system with multiplicative noise and multiple state delays.The main contributions are twofolds.First,in virtue of Pontryagin’s maximum principle,we solve the forward and backward stochastic difference equations(FBSDEs)and show the relationship between the state and the costate.Second,based on the solution to the FBSDEs and the coupled difference Riccati equations,the necessary and sufficient condition for the optimal problem is obtained.Meanwhile,an explicit analytical expression is given for the optimal LQG controller.Numerical examples are shown to illustrate the effectiveness of the proposed algorithm.展开更多
In this paper,we apply the collocation methods to a class of Volterra integral functional equations with multiple proportional delays(VIFEMPDs).We shall present the existence,uniqueness and regularity properties of an...In this paper,we apply the collocation methods to a class of Volterra integral functional equations with multiple proportional delays(VIFEMPDs).We shall present the existence,uniqueness and regularity properties of analytic solutions for this type of equations,and then analyze the convergence orders of the collocation solutions and give corresponding error estimates.The numerical results verify our theoretical analysis.展开更多
基金This work was supported by the National Natural Science Foundation of China(No. 60534010, 60572070), Liaoning Natural Science Foundation ofChina(No.20052027), and the Program for Changjiang Scholars and Innovative Research Team in University.
文摘The stability analysis of Cohen-Grossberg neural networks with multiple delays is given. An approach combining the Lyapunov functional with the linear matrix inequality (LMI) is taken to obtain the sufficient conditions for the globally asymptotic stability of equilibrium point. By using the properties of matrix norm, a practical corollary is derived. All results are established without assuming the differentiability and monotonicity of activation functions. The simulation samples have proved the effectiveness of the conclusions.
文摘New delay-independent and delay-dependent stability criteria for linear systems with multiple time-varying delays are established by using the time-domain method. The results are derived based on a new-type stability theorem for general retarded dynamical systems and new analysis techniques developed in the author's previous work. Unlike some results in the literature, all of the established results do not depend on the derivative of time-varying delays. Therefore, they are suitable for the case with very fast time-varying delays. In addition, some remarks are also given to explain the obtained results and to point out the limitations of the previous results in the literature. Keywords Stability - Delay-independent criteria - Delay-dependent criteria - Linear time-delay systems - Multiple time-varying delays This work was supported by NSFC Key-Project (No. 60334010) and Guangdong Province Natural Science Foundation of China (No. 31406).
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.
基金Project supported by the National Natural Science Foundation of China(Grant No.61803275)Liaoning Provincial Department of Education Scientific Research Fund Project,China(Grant Nos.lnjc202018 and lnzd202007)+1 种基金Liaoning BaiQianWan Talents Program(Grant No.2017076)Liaoning Province Doctor Starting Foundation(Grant No.20170520283).
文摘The idea of network splitting according to time delay and weight is introduced.Based on the cyber physical systems(CPS),a class of multi-weighted complex transportation networks with multiple delays is modeled.The finite-time synchronization of the proposed complex transportation networks model is studied systematically.On the basis of the theory of stability,the technique of adaptive control,aperiodically intermittent control and finite-time control,the aperiodically intermittent adaptive finite-time synchronization controller is designed.The controller designed in this paper is beneficial for understanding the synchronization in multi-weighted complex transportation networks with multiple delays.In addition,the conditions for the existence of finite time synchronization have been discussed in detail.And the specific value of the settling finite time for synchronization is obtained.Moreover,the outer coupling configuration matrices are not required to be irreducible or symmetric.Finally,simulation results of the finite-time synchronization problem are given to illustrate the correctness of the results obtained.
基金supported by the National Natural Science Foundation of China (Nos.10772112,10472065)the Key Project of Ministry of Education of China (No.107043)+2 种基金the Key Scientific Project of Shang-hai Municipal Education Commission (No.09ZZ17)the Specialized Research Fund for the DoctoralProgram of Higher Education of China (No.20070248032)the Research Project of State Key Laboratory of Ocean Engineering of China (No.GKZD010807)
文摘An optimal control method for seismic-excited building structures with multiple time delays is investigated in this paper. The system state equation with multiple time delays is discretized and transformed into a standard discrete form without any explicit time delay by a particular augmenting for state variables. A time-delay controller is then designed based on this standard equation using the discrete optimal control method. Effectiveness of the proposed controller is demonstrated by numerical simulations. Simulation results indicate that a very small time delay may result in the instability of the control system if it is not compensated in the control design. Time delay may be compensated effectively by the proposed controller, in the mean time, an effective control may be obtained. The proposed controller is valid for both small and large time delays.
基金the National Natural Science Foundation of China (No.60274017, 60325311).
文摘Global exponential stability problems are investigated for cellular neural networks (CNN) with multiple time-varying delays. Several new criteria in linear matrix inequality form or in algebraic form are presented to ascertain the uniqueness and global exponential stability of the equilibrium point for CNN with multiple time-varying delays and with constant time delays. The proposed method has the advantage of considering the difference of neuronal excitatory and inhibitory effects, which is also computationally efficient as it can be solved numerically using the recently developed interior-point algorithm or be checked using simple algebraic calculation. In addition, the proposed results generalize and improve upon some previous works. Two numerical examples are used to show the effectiveness of the obtained results.
基金The second author partially supported by NSFC (10571179, 10871203) GrantProgramfor New Century Excellent Talents in University of Ministry of Eduction of China
文摘By Fourier analysis techniques and Schauder fixed point theorem, we study the existence of periodic solutions for a class of even order differential equations with multiple delays. The result obtained is a generalization of the results developed by W. Layton to the case of multiple delays.
文摘The HIV problem is studied by version of delay mathematical models which consider the apoptosis of uninfected CD4<sup>+</sup> T cells which cultured with infected T cells in big volume. The opportunistic infection and the apoptosis of uninfected CD4<sup>+</sup> T cells are caused directly or indirectly by a toxic substance produced from HIV genes. Ubiquitously, the nonlinear incidence rate brings forth the increasing number of infected CD4<sup>+</sup> T cells with introduction of small time delay, and in addition, there also exists a natural time delay factor during the process of virus replication. With state feedback control of time delay, the bifurcating periodical oscillating phenomena is induced via Hopf bifurcation. Mathematically, with the geometrical criterion applied in the stability analysis of delay model, the critical threshold of Hopf bifurcation in multiple delay differential equations which satisfy the transversal condition is derived. By applying reduction dimensional method combined with the center manifold theory, the stability of the bifurcating periodical solution is analyzed by the perturbation near Hopf point.
文摘In this paper,we analyze the global dynamics of a neoclassical growth system incorporating patch structure and multiple pairs of time-varying delays.First,we derive the global existence,positiveness and boundedness of solutions for the addressed system.Then,by employing some novel differential inequality analyses and the fluctuation lemma,both delay-independent and delay-dependent criteria are established to ensure that all solutions are convergent to a unique positive equilibrium point vector,which does not possess the same components.Our results supplement and improve some existing results.Ultimately,some numerical examples are afforded to prove the effectiveness and feasibility of the theoretical findings.
文摘A system of delay differential equations is studied which represent a model for four neurons with time delayed connections between the neurons and time delayed feedback from each neuron to itself. The linear stability and bifurcation of the system are studied in a parameter space consisting of the sum of the time delays between the elements and the product of the strengths of the connections between the elements. Meanwhile, the bifurcation set are drawn in the parameter space.
基金supported by the National Basic Research Program of China (No. 2007CB714006)the National Natural Science Foundation(No. 61074020)
文摘In this paper,the robust stability issue of switched uncertain multidelay systems resulting from actuator failures is considered.Based on the average dwell time approach,a set of suitable switching signals is designed by using the total activation time ratio between the stable subsystem and the unstable one.It is first proven that the resulting closed-loop system is robustly exponentially stable for some allowable upper bound of delays if the nominal system with zero delay is exponentially stable under these switching laws.Particularly,the maximal upper bound of delays can be obtained from the linear matrix inequalities.At last,the effectiveness of the proposed method is demonstrated by a simulation example.
文摘The object of this article is to study the consequences of occurrence both fault in input and multiple time-varying delays simultaneously while designing observer to estimate the states of agents and also unknown nonlinear fault of system.Two delay dependent criteria are established to show the states of observer reach to states of MAS and also states of observer reach to consensus.From two obtained criteria,it can be deduced,by constructing a distributed controller-based observer design,MAS reach to consensus exponentially.Finally,the advantages of the obtained results are shown by solving an illustrative example.
文摘This paper is concerned with the optimal linear quadratic Gaussian(LQG)control problem for discrete time-varying system with multiplicative noise and multiple state delays.The main contributions are twofolds.First,in virtue of Pontryagin’s maximum principle,we solve the forward and backward stochastic difference equations(FBSDEs)and show the relationship between the state and the costate.Second,based on the solution to the FBSDEs and the coupled difference Riccati equations,the necessary and sufficient condition for the optimal problem is obtained.Meanwhile,an explicit analytical expression is given for the optimal LQG controller.Numerical examples are shown to illustrate the effectiveness of the proposed algorithm.
基金The first author is partially supported by forefront of science and interdisciplinary innovation projects of Jilin University and NNSF(No.11071102 of China).
文摘In this paper,we apply the collocation methods to a class of Volterra integral functional equations with multiple proportional delays(VIFEMPDs).We shall present the existence,uniqueness and regularity properties of analytic solutions for this type of equations,and then analyze the convergence orders of the collocation solutions and give corresponding error estimates.The numerical results verify our theoretical analysis.