Dear Editor,In this letter,several novel controllability results for a class of linear switched and impulsive systems are established.Different from the developed controllability conditions in most existing literature...Dear Editor,In this letter,several novel controllability results for a class of linear switched and impulsive systems are established.Different from the developed controllability conditions in most existing literature,the important role of switched and impulsive time sequence is considered.Applying the relevant geometric theory of matrix,a necessary and sufficient criterion for the controllability is firstly developed to judge when the controllability of such systems is affected by switched and impulsive time sequence.Furthermore,we further obtain a sufficient controllability condition that can be used to verify the controllability of such systems regardless of the switched and impulsive time sequence.Finally,a numerical example is given to verify the obtained theoretical results.展开更多
Dear Editor,This letter presents a class of saturated sliding mode control (SMC)strategy for linear systems subject to impulsive disturbance and input saturation. To ensure the feasibility of proposed SMC under satura...Dear Editor,This letter presents a class of saturated sliding mode control (SMC)strategy for linear systems subject to impulsive disturbance and input saturation. To ensure the feasibility of proposed SMC under saturation, a relationship is established among attraction domain, saturation structure and control gain.展开更多
By using the quasi-Lyapunov function, some sufficient conditions of global exponential stability for impulsive systems are established, which is the basis for the following discussion. Then, by employing Riccati inequ...By using the quasi-Lyapunov function, some sufficient conditions of global exponential stability for impulsive systems are established, which is the basis for the following discussion. Then, by employing Riccati inequality and Hamilton-Jacobi inequality approach, some sufficient conditions of robust exponential stability for uncertain linear/nonlinear impulsive systems are derived, respectively. Finally, some examples are given to illustrate the applications of the theory.展开更多
This paper investigates the exponential stability and performance analysis of nonlinear time-delay impulsive systems subject to actuator saturation. When continuous dynamics is unstable, under some conditions, it is s...This paper investigates the exponential stability and performance analysis of nonlinear time-delay impulsive systems subject to actuator saturation. When continuous dynamics is unstable, under some conditions, it is shown that the system can be stabilized by a class of saturated delayed-impulses regardless of the length of input delays. Conversely, when the system is originally stable, it is shown that under some conditions, the system is robust with respect to sufficient small delayed-impulses. Moreover, the design problem of the controller with the goal of obtaining a maximized estimate of the domain of attraction is formulated via a convex optimization problem. Three examples are provided to demonstrate the validity of the main results.展开更多
The problem of robust and reliable control design for linear uncertain impulsive systems with both timevarying norm-bounded parameter uncertainty and actuator failures was studied. The actuators are classified into tw...The problem of robust and reliable control design for linear uncertain impulsive systems with both timevarying norm-bounded parameter uncertainty and actuator failures was studied. The actuators are classified into two groups. One set of actuators susceptible to failures is possible to fail, the other set of actuators robust to failures is assumed never to fail. The outputs of the actuator failures are regarded as zero. The purpose is to design the state feedback controller such that, for all admissible uncertainties as well as actuator failures occurring among a prespecified subset of actuators, the plant remains asymptotically stable. A modified algebraic Riccati equation approach was developed to solve the problem addressed and a robust reliable control law was obtained. An numerical example was also offered to prove the effectiveness of the proposed method.展开更多
Dear Editor,This letter establishes several criteria for fixed-time stability and predefined-time stability of impulsive systems.First,sufficient conditions for fixed-time stability of impulsive systems are presented ...Dear Editor,This letter establishes several criteria for fixed-time stability and predefined-time stability of impulsive systems.First,sufficient conditions for fixed-time stability of impulsive systems are presented to treat the destabilizing impulses and hybrid impulses involving multiple jump maps by fixed-time control without linear feedback regulation.It determines the robustness of nonlinear systems against impulsive disturbance which has destabilizing and hybrid effect to dynamics.展开更多
In this paper, the dynamical behaviour of a linear impulsive system is discussed both theoretically and numerically. The existence and the stability of period-one solution are discussed by using a discrete map. The co...In this paper, the dynamical behaviour of a linear impulsive system is discussed both theoretically and numerically. The existence and the stability of period-one solution are discussed by using a discrete map. The conditions of existence for flip bifurcation are derived by using the centre manifold theorem and bifurcation theorem. The bifurcation analysis shows that chaotic solutions appear via a cascade of period-doubling in some interval of parameters. Moreover, the periodic solutions, the bifurcation diagram, and the chaotic attractor, which show their consistence with the theoretical analyses, are given in an example.展开更多
In this article,we present the existence,uniqueness,Ulam-Hyers stability and Ulam-Hyers-Rassias stability of semilinear nonautonomous integral causal evolution impulsive integro-delay dynamic systems on time scales,wi...In this article,we present the existence,uniqueness,Ulam-Hyers stability and Ulam-Hyers-Rassias stability of semilinear nonautonomous integral causal evolution impulsive integro-delay dynamic systems on time scales,with the help of a fixed point approach.We use Gronwall’s inequality on time scales,an abstract Growall’s lemma and a Picard operator as basic tools to develop our main results.To overcome some difficulties,we make a variety of assumptions.At the end an example is given to demonstrate the validity of our main theoretical results.展开更多
This paper investigates robust filter design for linear discrete-time impulsive systems with uncertainty under H∞ performance. First, an impulsive linear filter and a robust H∞ filtering problem are introduced for a...This paper investigates robust filter design for linear discrete-time impulsive systems with uncertainty under H∞ performance. First, an impulsive linear filter and a robust H∞ filtering problem are introduced for a discrete-time impulsive systems. Then, a sufficient condition of asymptotical stability and H∞ performance for the filtering error systems are provided by the discrete-time Lyapunov function method. The filter gains can be obtained by solving a set of linear matrix inequalities （LMIs）. Finally, a numerical example is presented to show effectiveness of the obtained result.展开更多
Stability criteria for the complex-valued impulsive system are applied widely in many fields, such as quantum systems, which have been studied in recent decades. In this paper, I investigate the Lyapunov control of fi...Stability criteria for the complex-valued impulsive system are applied widely in many fields, such as quantum systems, which have been studied in recent decades. In this paper, I investigate the Lyapunov control of finite dimensional complex-valued systems with impulsive control fields, where the studied complex-valued systems are governed by the Schrödinger equation and can be used in quantum systems. By one Lyapunov function based on state error and the invariant principle of impulsive systems, I study the convergence of complex-valued systems with impulsive control fields and propose new results for the mentioned complex-valued systems in the form of sufficient conditions. A numerical simulation to validate the proposed control method is provided.展开更多
In this paper,the problem of dynamic event-triggered impulsive control for a class of nonlinear systems is studied.Based on the input-to-state stability results of nonlinear systems,a dynamic event-triggered control s...In this paper,the problem of dynamic event-triggered impulsive control for a class of nonlinear systems is studied.Based on the input-to-state stability results of nonlinear systems,a dynamic event-triggered control strategy is designed to stabilize the nonlinear system,and the lower bound of triggering is set.By using Lyapunov method,a sufficient condition for the stabilization of nonlinear systems is obtained.The conservation of the original theorem is maintained while the number of transmissions is greatly reduced.Numerical simulations show the effectiveness of the theoretical results.展开更多
This paper is aimed at stabilising control for impulsive systems via the state feedback.Firstly.stability analysls for the closed-loop system is conducted using a Lyapunov-like functional(LLK)thatis not necessarily co...This paper is aimed at stabilising control for impulsive systems via the state feedback.Firstly.stability analysls for the closed-loop system is conducted using a Lyapunov-like functional(LLK)thatis not necessarily continuous nor positive definite.Built on two subintervals of the impulsive interval being separated by the current,'instant,a cot multiple integrals of thestate os5termsamong the integrals,thestate andin icrete LLK is constructed by introducing npulsivestates.Integral equatio ns of the imp Stem are exploited and higrt-onder nequalities are taken when e imtior min Ve of the LLK.New stabil al dwell-timemaximal dwelt the stabilising control prot biref Skel serme ar eobrnianer vell-time are obtalned.Se inequaltyndet results nerica examples illustrate that the stability results are less cons for impulsive systems is valid.展开更多
Dear Editor,This letter deals with the stabilization problem of nonlinear stochastic systems via self-triggered impulsive control(STIC), where the timing of impulsive control actions is not dependent on continuous sta...Dear Editor,This letter deals with the stabilization problem of nonlinear stochastic systems via self-triggered impulsive control(STIC), where the timing of impulsive control actions is not dependent on continuous state monitoring. In contrast to the existing self-triggered control method, novel self-triggered mechanism(STM) is proposed by incorporating a waiting time for stabilizing impulses. This allows for direct prediction of the next impulsive instant.展开更多
Dear Editor,This letter studies finite-time stability (FTS) of impulsive and switched hybrid systems with delay-dependent impulses. Some conditions, based on Lyapunov method, are proposed for ensuring FTS and estimati...Dear Editor,This letter studies finite-time stability (FTS) of impulsive and switched hybrid systems with delay-dependent impulses. Some conditions, based on Lyapunov method, are proposed for ensuring FTS and estimating settling-time function (STF) of the hybrid systems.When switching dynamics are FTS and impulsive dynamics involve destabilizing delay-dependent impulses, the FTS is retained if the impulses occur infrequently.展开更多
Dear Editor,This letter studies a real-world issue in leader-follower multi-agent systems(MASs)named open topology,which permits the variations of agent set and network connections.Specially,a novel transition process...Dear Editor,This letter studies a real-world issue in leader-follower multi-agent systems(MASs)named open topology,which permits the variations of agent set and network connections.Specially,a novel transition process is developed to explain how the involved variation of network scale affects the dynamic behavior of the MASs.From a resource limited perspective,the distributed saturated impulsive control is then designed,under which some sufficient criteria are integrated into local quasi-consensus performance.We also provide a combined optimization algorithm for all agents to make the estimated domain of initial errors closer to the real one,thereby resulting in less conservativeness.Finally,a numerical example validates our results.展开更多
Considering that actual systems are often constrained by multiple factors such as state limitation,actuator saturation and actuator failure at the same time,this paper provides an effective solution for non-affine mul...Considering that actual systems are often constrained by multiple factors such as state limitation,actuator saturation and actuator failure at the same time,this paper provides an effective solution for non-affine multi-player systems,which can guarantee the required performance while saving communication cost.Initially,an auxiliary system is established to accommodate state limitations,following which the controller design is partitioned into two distinct segments,addressing different types of faults.Specifically,the discontinuous and continuous aspects of the controller are achieved by sliding-mode control(SMC)and adaptive critic design(ACD),respectively.During the implementation of ACD to solve the guaranteed value function incorporating the utility function designed for the asymmetric saturation of the control input,two adaptive schemes including adaptive eventtriggered impulsive control(AETIC)and adaptive self-triggered impulsive control(ASTIC)are introduced successively.It is proved that the system maintains exponential stability rather than asymptotic stability and the state signals keep ultimately uniformly bounded(UUB).Finally,the effectiveness of the proposed control sequence is verified by simulation comparisons.展开更多
Dear Editor,This letter investigates predefined-time optimization problems(OPs) of multi-agent systems(MASs), where the agent of MASs is subject to inequality constraints, and the team objective function accounts for ...Dear Editor,This letter investigates predefined-time optimization problems(OPs) of multi-agent systems(MASs), where the agent of MASs is subject to inequality constraints, and the team objective function accounts for impulse effects. Firstly, to address the inequality constraints,the penalty method is introduced. Then, a novel optimization strategy is developed, which only requires that the team objective function be strongly convex.展开更多
This paper studies the existence, uniqueness, and stability of solutions for stochastic impulsive systems. By employing Lyapunov-like functions, some sufficient conditions of the global existence, uniqueness, and stab...This paper studies the existence, uniqueness, and stability of solutions for stochastic impulsive systems. By employing Lyapunov-like functions, some sufficient conditions of the global existence, uniqueness, and stability of solutions for stochastic impulsive systems are established. Furthermore, the results are specialized to the case of linear stochastic impulsive systems. Finally, some examples are given to illustrate the applications of our theory.展开更多
This paper studies the stochastic asymptotical stability of stochastic impulsive differential equations, and establishes a comparison theory to ensure the trivial solution＇s stochastic asymptotical stability. From th...This paper studies the stochastic asymptotical stability of stochastic impulsive differential equations, and establishes a comparison theory to ensure the trivial solution＇s stochastic asymptotical stability. From the comparison theory, it can find out whether the stochastic impulsive differential system is stable just by studying the stability of a deterministic comparison system. As a general application of this theory, it controls the chaos of stochastic Lii system using impulsive control method, and numerical simulations are employed to verify the feasibility of this method.展开更多
In the area of control theory the time-delay systems have been investigated. It's well known that delays often result in instability, therefore, stability analysis of time-delay systems is an important subject in ...In the area of control theory the time-delay systems have been investigated. It's well known that delays often result in instability, therefore, stability analysis of time-delay systems is an important subject in control theory. As a result, many criteria for testing the stability of linear time-delay systems have been proposed. Significant progress has been made in the theory of impulsive systems and impulsive delay systems in recent years. However, the corresponding theory for uncertain impulsive systems and uncertain impulsive delay systems has not been fully developed. In this paper, robust stability criteria are established for uncertain linear delay impulsive systems by using Lyapunov function, Razumikhin techniques and the results obtained. Some examples are given to illustrate our theory.展开更多
基金supported in part by the National Natural Science Foundation of China(62322311,62303162,62233007,62203157)the Technology Development Program of Henan Province(242102211052).
文摘Dear Editor,In this letter,several novel controllability results for a class of linear switched and impulsive systems are established.Different from the developed controllability conditions in most existing literature,the important role of switched and impulsive time sequence is considered.Applying the relevant geometric theory of matrix,a necessary and sufficient criterion for the controllability is firstly developed to judge when the controllability of such systems is affected by switched and impulsive time sequence.Furthermore,we further obtain a sufficient controllability condition that can be used to verify the controllability of such systems regardless of the switched and impulsive time sequence.Finally,a numerical example is given to verify the obtained theoretical results.
基金supported by the National Natural Science Foundation of China(62173215)the Major Basic Research Program of the Natural Science Foundation of Shandong Province in China(ZR2021ZD04,ZR2020ZD24)
文摘Dear Editor,This letter presents a class of saturated sliding mode control (SMC)strategy for linear systems subject to impulsive disturbance and input saturation. To ensure the feasibility of proposed SMC under saturation, a relationship is established among attraction domain, saturation structure and control gain.
文摘By using the quasi-Lyapunov function, some sufficient conditions of global exponential stability for impulsive systems are established, which is the basis for the following discussion. Then, by employing Riccati inequality and Hamilton-Jacobi inequality approach, some sufficient conditions of robust exponential stability for uncertain linear/nonlinear impulsive systems are derived, respectively. Finally, some examples are given to illustrate the applications of the theory.
基金supported by National Natural Science Foundation of China (62173215)Major Basic Research Program of the Natural Science Foundation of Shandong Province in China(ZR2021ZD04, ZR2020ZD24)the Support Plan for Outstanding Youth Innovation Team in Shandong Higher Education Institutions (2019KJI008)。
文摘This paper investigates the exponential stability and performance analysis of nonlinear time-delay impulsive systems subject to actuator saturation. When continuous dynamics is unstable, under some conditions, it is shown that the system can be stabilized by a class of saturated delayed-impulses regardless of the length of input delays. Conversely, when the system is originally stable, it is shown that under some conditions, the system is robust with respect to sufficient small delayed-impulses. Moreover, the design problem of the controller with the goal of obtaining a maximized estimate of the domain of attraction is formulated via a convex optimization problem. Three examples are provided to demonstrate the validity of the main results.
基金Project (60474003) supported by the National Natural Science Foundation of China
文摘The problem of robust and reliable control design for linear uncertain impulsive systems with both timevarying norm-bounded parameter uncertainty and actuator failures was studied. The actuators are classified into two groups. One set of actuators susceptible to failures is possible to fail, the other set of actuators robust to failures is assumed never to fail. The outputs of the actuator failures are regarded as zero. The purpose is to design the state feedback controller such that, for all admissible uncertainties as well as actuator failures occurring among a prespecified subset of actuators, the plant remains asymptotically stable. A modified algebraic Riccati equation approach was developed to solve the problem addressed and a robust reliable control law was obtained. An numerical example was also offered to prove the effectiveness of the proposed method.
基金This work was supported in part by the National Natural Science Foundation of China(62203284,62173215)the Natural Science Foundation of Shandong Province(ZR2021QF048)the Major Basic Research Program of the Natural Science Foundation of Shandong Province in China(ZR2021ZD04,ZR2020ZD24).
文摘Dear Editor,This letter establishes several criteria for fixed-time stability and predefined-time stability of impulsive systems.First,sufficient conditions for fixed-time stability of impulsive systems are presented to treat the destabilizing impulses and hybrid impulses involving multiple jump maps by fixed-time control without linear feedback regulation.It determines the robustness of nonlinear systems against impulsive disturbance which has destabilizing and hybrid effect to dynamics.
基金Project supported by the National Natural Science Foundation of China (Grant Nos 10572011, 100461002, and 10661005)the Natural Science Foundation of Guangxi Province, China (Grant Nos 0575092 and 0832244)
文摘In this paper, the dynamical behaviour of a linear impulsive system is discussed both theoretically and numerically. The existence and the stability of period-one solution are discussed by using a discrete map. The conditions of existence for flip bifurcation are derived by using the centre manifold theorem and bifurcation theorem. The bifurcation analysis shows that chaotic solutions appear via a cascade of period-doubling in some interval of parameters. Moreover, the periodic solutions, the bifurcation diagram, and the chaotic attractor, which show their consistence with the theoretical analyses, are given in an example.
基金supported by Talent Project of Chongqing Normal University(02030307-0040)the China Posdoctoral Science Foundation(2019M652348)+1 种基金Natural Science Foundation of Chongqing(cstc2020jcyj-msxm X0123)Technology Research Foundation of Chongqing Educational Committee(KJQN202000528,KJQN201900539)。
文摘In this article,we present the existence,uniqueness,Ulam-Hyers stability and Ulam-Hyers-Rassias stability of semilinear nonautonomous integral causal evolution impulsive integro-delay dynamic systems on time scales,with the help of a fixed point approach.We use Gronwall’s inequality on time scales,an abstract Growall’s lemma and a Picard operator as basic tools to develop our main results.To overcome some difficulties,we make a variety of assumptions.At the end an example is given to demonstrate the validity of our main theoretical results.
基金supported by the National Natural Science Foundation of China (No. 60874027)
文摘This paper investigates robust filter design for linear discrete-time impulsive systems with uncertainty under H∞ performance. First, an impulsive linear filter and a robust H∞ filtering problem are introduced for a discrete-time impulsive systems. Then, a sufficient condition of asymptotical stability and H∞ performance for the filtering error systems are provided by the discrete-time Lyapunov function method. The filter gains can be obtained by solving a set of linear matrix inequalities （LMIs）. Finally, a numerical example is presented to show effectiveness of the obtained result.
文摘Stability criteria for the complex-valued impulsive system are applied widely in many fields, such as quantum systems, which have been studied in recent decades. In this paper, I investigate the Lyapunov control of finite dimensional complex-valued systems with impulsive control fields, where the studied complex-valued systems are governed by the Schrödinger equation and can be used in quantum systems. By one Lyapunov function based on state error and the invariant principle of impulsive systems, I study the convergence of complex-valued systems with impulsive control fields and propose new results for the mentioned complex-valued systems in the form of sufficient conditions. A numerical simulation to validate the proposed control method is provided.
基金supported by the Natural Science Foundation of Shandong Province(ZR2023MA065)City-University Integration Development Strategy Project of Jinan(JNSX2024014).
文摘In this paper,the problem of dynamic event-triggered impulsive control for a class of nonlinear systems is studied.Based on the input-to-state stability results of nonlinear systems,a dynamic event-triggered control strategy is designed to stabilize the nonlinear system,and the lower bound of triggering is set.By using Lyapunov method,a sufficient condition for the stabilization of nonlinear systems is obtained.The conservation of the original theorem is maintained while the number of transmissions is greatly reduced.Numerical simulations show the effectiveness of the theoretical results.
基金supported by National Natural Science Foundation of China[grant number 62373214].
文摘This paper is aimed at stabilising control for impulsive systems via the state feedback.Firstly.stability analysls for the closed-loop system is conducted using a Lyapunov-like functional(LLK)thatis not necessarily continuous nor positive definite.Built on two subintervals of the impulsive interval being separated by the current,'instant,a cot multiple integrals of thestate os5termsamong the integrals,thestate andin icrete LLK is constructed by introducing npulsivestates.Integral equatio ns of the imp Stem are exploited and higrt-onder nequalities are taken when e imtior min Ve of the LLK.New stabil al dwell-timemaximal dwelt the stabilising control prot biref Skel serme ar eobrnianer vell-time are obtalned.Se inequaltyndet results nerica examples illustrate that the stability results are less cons for impulsive systems is valid.
基金supported by the National Natural Science Foundation of China(62403393,12202058,62103118)the China Postdoctoral Science Foundation(2021T140160,2023 T160051)the Natural Science Foundation of Chongqing(CSTB 2023NSCQ-MSX0152)
文摘Dear Editor,This letter deals with the stabilization problem of nonlinear stochastic systems via self-triggered impulsive control(STIC), where the timing of impulsive control actions is not dependent on continuous state monitoring. In contrast to the existing self-triggered control method, novel self-triggered mechanism(STM) is proposed by incorporating a waiting time for stabilizing impulses. This allows for direct prediction of the next impulsive instant.
基金supported by the National Natural Science Foundation of China(61833005)
文摘Dear Editor,This letter studies finite-time stability (FTS) of impulsive and switched hybrid systems with delay-dependent impulses. Some conditions, based on Lyapunov method, are proposed for ensuring FTS and estimating settling-time function (STF) of the hybrid systems.When switching dynamics are FTS and impulsive dynamics involve destabilizing delay-dependent impulses, the FTS is retained if the impulses occur infrequently.
基金supported by the Natural Science Foundation of Jiangsu Province(BK20240009)the National Natural Science Foundation of China(62373105,62373262)Jiangsu Provincial Scientific Research Center of Applied Mathematics(BK20233002).
文摘Dear Editor,This letter studies a real-world issue in leader-follower multi-agent systems(MASs)named open topology,which permits the variations of agent set and network connections.Specially,a novel transition process is developed to explain how the involved variation of network scale affects the dynamic behavior of the MASs.From a resource limited perspective,the distributed saturated impulsive control is then designed,under which some sufficient criteria are integrated into local quasi-consensus performance.We also provide a combined optimization algorithm for all agents to make the estimated domain of initial errors closer to the real one,thereby resulting in less conservativeness.Finally,a numerical example validates our results.
基金supported in part by the National Natural Science Foundation of China(62273036,62403045)the Open Research Fund of the State Key Laboratory of Multimodal Artificial Intelligence Systems(MAIS2025020)Interdisciplinary Research Project for Young Teachers of USTB(Fundamental Research Funds for the Central Universities)(FRF-IDRY-23-036).
文摘Considering that actual systems are often constrained by multiple factors such as state limitation,actuator saturation and actuator failure at the same time,this paper provides an effective solution for non-affine multi-player systems,which can guarantee the required performance while saving communication cost.Initially,an auxiliary system is established to accommodate state limitations,following which the controller design is partitioned into two distinct segments,addressing different types of faults.Specifically,the discontinuous and continuous aspects of the controller are achieved by sliding-mode control(SMC)and adaptive critic design(ACD),respectively.During the implementation of ACD to solve the guaranteed value function incorporating the utility function designed for the asymmetric saturation of the control input,two adaptive schemes including adaptive eventtriggered impulsive control(AETIC)and adaptive self-triggered impulsive control(ASTIC)are introduced successively.It is proved that the system maintains exponential stability rather than asymptotic stability and the state signals keep ultimately uniformly bounded(UUB).Finally,the effectiveness of the proposed control sequence is verified by simulation comparisons.
基金supported in part by the National Natural Science Foundation of China(62276119)the Natural Science Foundation of Jiangsu Province(BK20241764)the Postgraduate Research & Practice Innovation Program of Jiangsu Province(KYCX22_2860)
文摘Dear Editor,This letter investigates predefined-time optimization problems(OPs) of multi-agent systems(MASs), where the agent of MASs is subject to inequality constraints, and the team objective function accounts for impulse effects. Firstly, to address the inequality constraints,the penalty method is introduced. Then, a novel optimization strategy is developed, which only requires that the team objective function be strongly convex.
基金This research is supported by the National Natural Science Foundation of China under Grant No. 60274007, and the Post Doctoral Foundation of China and the Excellent Young Program of the Education Department of Hunan Province under Grant No. 04B068, and the NSERC-Canada.
文摘This paper studies the existence, uniqueness, and stability of solutions for stochastic impulsive systems. By employing Lyapunov-like functions, some sufficient conditions of the global existence, uniqueness, and stability of solutions for stochastic impulsive systems are established. Furthermore, the results are specialized to the case of linear stochastic impulsive systems. Finally, some examples are given to illustrate the applications of our theory.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10902085)
文摘This paper studies the stochastic asymptotical stability of stochastic impulsive differential equations, and establishes a comparison theory to ensure the trivial solution＇s stochastic asymptotical stability. From the comparison theory, it can find out whether the stochastic impulsive differential system is stable just by studying the stability of a deterministic comparison system. As a general application of this theory, it controls the chaos of stochastic Lii system using impulsive control method, and numerical simulations are employed to verify the feasibility of this method.
基金This project was supported by the National Natural Science Foundation of China (60274007) NSERC-Canada.
文摘In the area of control theory the time-delay systems have been investigated. It's well known that delays often result in instability, therefore, stability analysis of time-delay systems is an important subject in control theory. As a result, many criteria for testing the stability of linear time-delay systems have been proposed. Significant progress has been made in the theory of impulsive systems and impulsive delay systems in recent years. However, the corresponding theory for uncertain impulsive systems and uncertain impulsive delay systems has not been fully developed. In this paper, robust stability criteria are established for uncertain linear delay impulsive systems by using Lyapunov function, Razumikhin techniques and the results obtained. Some examples are given to illustrate our theory.
