This paper investigates the problem of event-triggered finite-time <i>H</i><sub>∞</sub> control for a class of switched stochastic systems. The main objective of this study is to design an eve...This paper investigates the problem of event-triggered finite-time <i>H</i><sub>∞</sub> control for a class of switched stochastic systems. The main objective of this study is to design an event-triggered state feedback <i>H</i><sub>∞</sub> controller such that the resulting closed-loop system is finite-time bounded and satisfies a prescribed <i>H</i><sub>∞</sub> level in some given finite-time interval. Based on stochastic differential equations theory and average dwell time approach, sufficient conditions are derived to ensure the finite-time stochastic stability with the prescribed <i>H</i><sub>∞</sub> performance for the relevant closed-loop system by employing the linear matrix inequality technique. Finally, the desired state feedback <i>H</i><sub>∞</sub> controller gain matrices can be expressed in an explicit form.展开更多
In this paper, the stability properties for a class of switched stochastic systems with commutative componentwise subsystem matrices are studied. Under some switching law, the trivial solutions of the above systems ar...In this paper, the stability properties for a class of switched stochastic systems with commutative componentwise subsystem matrices are studied. Under some switching law, the trivial solutions of the above systems are proved to be exponentially stable in mean square and almost sure exponentially stable if the random perturbations are sufficiently “small”.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
Compared with the classical Markov repairable system, the Markov repairable system with stochastic regimes switching introduced in the paper provides a more realistic description of the practical system. The system ca...Compared with the classical Markov repairable system, the Markov repairable system with stochastic regimes switching introduced in the paper provides a more realistic description of the practical system. The system can be used to model the dynamics of a repairable system whose performance regimes switch according to the external conditions. For example, to satisfy the demand variation that is typical for the power and communication systems and reduce the cost, these systems usually adjust their operating regimes. The transition rate matrices under distinct operating regimes are assumed to be different and the sojourn times in distinct regimes are governed by a finite state Markov chain. By using the theory of Markov process, Ion channel theory, and Laplace transforms, the up time of the system are studied. A numerical example is given to illustrate the obtained results. The effect of sojourn times in distinct regimes on the availability and the up time are also discussed in the numerical example.展开更多
This paper mainly tends to utilize Razumikhin-type theorems to investigate p-th moment stability for a class of stochastic switching nonlinear systems with delay. Based on the Lyapunov-Razumik- hin methods, some suffi...This paper mainly tends to utilize Razumikhin-type theorems to investigate p-th moment stability for a class of stochastic switching nonlinear systems with delay. Based on the Lyapunov-Razumik- hin methods, some sufficient conditions are derived to check the stability of stochastic switching nonlinear systems with delay. One numerical example is provided to demonstrate the effectiveness of the results.展开更多
This paper mainly investigates dynamics behavior of HIV (human immunodeficiency virus) infectious disease model with switching parameters, and combined bounded noise and Gaussian white noise. This model is different...This paper mainly investigates dynamics behavior of HIV (human immunodeficiency virus) infectious disease model with switching parameters, and combined bounded noise and Gaussian white noise. This model is different from existing HIV models. Based on stochastic Ito lemma and Razumikhin-type approach, some threshold conditions are established to guarantee the disease eradication or persistence. Results show that the smaller amplitude of bounded noise and R0 〈 1 can cause the disease to die out; the disease becomes persistent if R0 〉 1. Moreover, it is found that larger noise intensity suppresses the prevalence of the disease even if R0 〉 1. Some numerical examples are given to verify the obtained results.展开更多
This paper addresses the problem of the design of controller for fuzzy semi-Markov jump systems with hidden modes against the incomplete information on probability density functions of sojourn time. Two ubiquitous cir...This paper addresses the problem of the design of controller for fuzzy semi-Markov jump systems with hidden modes against the incomplete information on probability density functions of sojourn time. Two ubiquitous circumstances in practice are taken into account, which are often ignored in other related work:(1) the phenomenon that system modes cannot be accessed entirely is considered proactively;(2) finitely accessible information on probability density functions is studied in this paper. By virtue of hidden semi-Markov chain, the underlying systems are modeled as hidden semi-Markov jump systems, which are more general than semi-Markov jump systems. Sufficient conditions on the existence of desired accessible-mode-dependent fuzzy controller are derived such that the fuzzy hidden semi-Markov jump systems is mean square stable. Based on the emission probability matrix, the presented control policy overcomes the possible mode-mismatch between the system mode and the accessible mode.Finally, an example is provided to demonstrate the effectiveness of the proposed control method.展开更多
In this paper, we derive the stochastic maximum principle for optimal control problems of the forward-backward Markovian regime-switching system. The control system is described by an anticipated forward-backward stoc...In this paper, we derive the stochastic maximum principle for optimal control problems of the forward-backward Markovian regime-switching system. The control system is described by an anticipated forward-backward stochastic pantograph equation and modulated by a continuous-time finite-state Markov chain. By virtue of classical variational approach, duality method, and convex analysis, we obtain a stochastic maximum principle for the optimal control.展开更多
Switching Markov jump linear system(SMJLS),a special hybrid system,has attracted a lot of studies recently.SMJLS is governed by stochastic and deterministic commutations.This paper focuses on the switching strategy wh...Switching Markov jump linear system(SMJLS),a special hybrid system,has attracted a lot of studies recently.SMJLS is governed by stochastic and deterministic commutations.This paper focuses on the switching strategy which stabilizes the SMJLS in a finite time interval in order to further expand the existing results and investigate new aspects of such systems.Several sufficient conditions for finite-time stability of discrete-time SMJLS are provided,and the numerical problems in these sufficient conditions are solved by solving linear matrix inequalities(LMIs).Finally,numerical examples are given to show the feasibility and effectiveness of the results.展开更多
文摘This paper investigates the problem of event-triggered finite-time <i>H</i><sub>∞</sub> control for a class of switched stochastic systems. The main objective of this study is to design an event-triggered state feedback <i>H</i><sub>∞</sub> controller such that the resulting closed-loop system is finite-time bounded and satisfies a prescribed <i>H</i><sub>∞</sub> level in some given finite-time interval. Based on stochastic differential equations theory and average dwell time approach, sufficient conditions are derived to ensure the finite-time stochastic stability with the prescribed <i>H</i><sub>∞</sub> performance for the relevant closed-loop system by employing the linear matrix inequality technique. Finally, the desired state feedback <i>H</i><sub>∞</sub> controller gain matrices can be expressed in an explicit form.
基金Supported by the National Natural Science Foundation of China under Grant 10461001.
文摘In this paper, the stability properties for a class of switched stochastic systems with commutative componentwise subsystem matrices are studied. Under some switching law, the trivial solutions of the above systems are proved to be exponentially stable in mean square and almost sure exponentially stable if the random perturbations are sufficiently “small”.
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.
基金supported by the National Natural Science Foundation of China (71071020 60705036)Beijing Excellent Doctoral Dissertation Instructor Project of Humanities and Social Sciences(yb20091000701)
文摘Compared with the classical Markov repairable system, the Markov repairable system with stochastic regimes switching introduced in the paper provides a more realistic description of the practical system. The system can be used to model the dynamics of a repairable system whose performance regimes switch according to the external conditions. For example, to satisfy the demand variation that is typical for the power and communication systems and reduce the cost, these systems usually adjust their operating regimes. The transition rate matrices under distinct operating regimes are assumed to be different and the sojourn times in distinct regimes are governed by a finite state Markov chain. By using the theory of Markov process, Ion channel theory, and Laplace transforms, the up time of the system are studied. A numerical example is given to illustrate the obtained results. The effect of sojourn times in distinct regimes on the availability and the up time are also discussed in the numerical example.
文摘This paper mainly tends to utilize Razumikhin-type theorems to investigate p-th moment stability for a class of stochastic switching nonlinear systems with delay. Based on the Lyapunov-Razumik- hin methods, some sufficient conditions are derived to check the stability of stochastic switching nonlinear systems with delay. One numerical example is provided to demonstrate the effectiveness of the results.
基金supported by the National Natural Science Foundation of China(Grant Nos.11172233,11472212,11272258,and 11302170)the Natural Science and Engineering Research Council of Canada(NSERC)
文摘This paper mainly investigates dynamics behavior of HIV (human immunodeficiency virus) infectious disease model with switching parameters, and combined bounded noise and Gaussian white noise. This model is different from existing HIV models. Based on stochastic Ito lemma and Razumikhin-type approach, some threshold conditions are established to guarantee the disease eradication or persistence. Results show that the smaller amplitude of bounded noise and R0 〈 1 can cause the disease to die out; the disease becomes persistent if R0 〉 1. Moreover, it is found that larger noise intensity suppresses the prevalence of the disease even if R0 〉 1. Some numerical examples are given to verify the obtained results.
基金supported by the National Defense Basic Scientific Research Program of China (Grant No. JCKY2018603C015)the Cultivation Plan of Major Research Program of Harbin Institute of Technology (Grant No.ZDXMPY20180101)Open Project Program of Key Laboratory of Ministry of Education of System Control and Information Processing (Grant No.SCIP202002)。
文摘This paper addresses the problem of the design of controller for fuzzy semi-Markov jump systems with hidden modes against the incomplete information on probability density functions of sojourn time. Two ubiquitous circumstances in practice are taken into account, which are often ignored in other related work:(1) the phenomenon that system modes cannot be accessed entirely is considered proactively;(2) finitely accessible information on probability density functions is studied in this paper. By virtue of hidden semi-Markov chain, the underlying systems are modeled as hidden semi-Markov jump systems, which are more general than semi-Markov jump systems. Sufficient conditions on the existence of desired accessible-mode-dependent fuzzy controller are derived such that the fuzzy hidden semi-Markov jump systems is mean square stable. Based on the emission probability matrix, the presented control policy overcomes the possible mode-mismatch between the system mode and the accessible mode.Finally, an example is provided to demonstrate the effectiveness of the proposed control method.
文摘In this paper, we derive the stochastic maximum principle for optimal control problems of the forward-backward Markovian regime-switching system. The control system is described by an anticipated forward-backward stochastic pantograph equation and modulated by a continuous-time finite-state Markov chain. By virtue of classical variational approach, duality method, and convex analysis, we obtain a stochastic maximum principle for the optimal control.
基金the National Natural Science Foundation of China(No.61573237)the“111 Project”(No.D18003)the Program of China Scholarship Council(No.201906895021)。
文摘Switching Markov jump linear system(SMJLS),a special hybrid system,has attracted a lot of studies recently.SMJLS is governed by stochastic and deterministic commutations.This paper focuses on the switching strategy which stabilizes the SMJLS in a finite time interval in order to further expand the existing results and investigate new aspects of such systems.Several sufficient conditions for finite-time stability of discrete-time SMJLS are provided,and the numerical problems in these sufficient conditions are solved by solving linear matrix inequalities(LMIs).Finally,numerical examples are given to show the feasibility and effectiveness of the results.