Moment exponential stability analysis of Markovian jump stochastic differential equations with uncertain transition jump rates

This paper is concerned with the moment exponential stability analysis of Markovian jump stochastic differential equations. The equations under consideration are more general, whose transition jump rates matrix Q is not precisely known. Sufficient conditions for testing the stability of such equations are established, and some numerical examples to illustrate the effectiveness of our results are presented.     

Stochastic stability and stabilization of discrete‐time singular Markovian jump systems with partially unknown transition probabilities

This paper considers the stochastic stability and stabilization of discrete‐time singular Markovian jump systems with partially unknown transition probabilities. Firstly, a set of necessary and sufficient conditions for the stochastic stability is proposed in terms of LMIs, then a set of sufficient conditions is proposed for the design of a state feedback controller to guarantee that the corresponding closed‐loop systems are regular, causal, and stochastically stable by employing the LMI technique. Finally, some examples are provided to demonstrate the effectiveness of the proposed approaches. Copyright © 2014 John Wiley & Sons, Ltd.     

Robust exponential stabilization for Markovian jump systems with mode-dependent input delay

This paper is concerned with the problem of exponential stabilization for uncertain linear systems with Markovian jump parameters and mode-dependent input delays. Sufficient stabilization conditions are developed in terms of matrix inequalities, which can be solved by a proposed iterative algorithm based on the cone complementarity linearization (CCL) method. Memory controllers are also designed such that the closed-loop system is exponentially mean-square stable for all admissible uncertainties. Numerical examples are given to show that the developed method is efficient and less conservative.     

Improved exponential stability for stochastic Markovian jump systems with nonlinearity and time‐varying delay

This paper is concerned with delay‐dependent exponential stability for stochastic Markovian jump systems with nonlinearity and time‐varying delay. An improved exponential stability criterion for stochastic Markovian jump systems with nonlinearity and time‐varying delay is proposed without ignoring any terms by considering the relationship among the time‐varying delay, its upper bound and their difference, and using both Itô's differential formula and Lyapunov stability theory. A numerical example is given to illustrate the effectiveness and the benefits of the proposed method. Copyright © 2009 John Wiley & Sons, Ltd.     

Control of Markovian jump discrete-time systems with norm boundeduncertainty and unknown delay

This paper studies the problem of control for discrete time delay linear systems with Markovian jump parameters. The system under consideration is subjected to both time-varying norm-bounded parameter uncertainty and unknown time delay in the state, and Markovian jump parameters in all system matrices. We address the problem of robust state feedback control in which both robust stochastic stability and a prescribed H_∞ performance are required to be achieved irrespective of the uncertainty and time delay. It is shown that the above problem can be solved if a set of coupled linear matrix inequalities has a solution     

New results on stability analysis and stabilization of time‐delay continuous Markovian jump systems with partially known rates matrix

In this note, the problems of stability analysis and controller synthesis of Markovian jump systems with time‐varying delay and partially known transition rates are investigated via an input–output approach. First, the system under consideration is transformed into an interconnected system, and new results on stochastic scaled small‐gain condition for stochastic interconnected systems are established, which are crucial for the problems considered in this paper. Based on the system transformation and the stochastic scaled small‐gain theorem, stochastic stability of the original system is examined via the stochastic version of the bounded realness of the transformed forward system. The merit of the proposed approach lies in its reduced conservatism, which is made possible by a precise approximation of the time‐varying delay and the new result on the stochastic scaled small‐gain theorem. The proposed stability condition is demonstrated to be much less conservative than most existing results. Moreover, the problem of stabilization is further solved with an admissible controller designed via convex optimizations, whose effectiveness is also illustrated via numerical examples. Copyright © 2015 John Wiley & Sons, Ltd.     

Delay-dependent criteria for robust stability of linear neutral systems with time-varying delay and nonlinear perturbations

This article investigates the robust stability of linear neutral systems with time-varying delay and nonlinear perturbations. Using a new Lyapunov–Krasovskii functional and employing some free weighting matrices, less conservative delay-dependent robust stability conditions for such systems in terms of linear matrix inequalities are derived. Numerical examples are given to indicate significant improvements over some existing results.     

Stability and stabilization of Markovian jump linear systems with partly unknown transition probabilities

In this paper, the stability and stabilization problems of a class of continuous-time and discrete-time Markovian jump linear system (MJLS) with partly unknown transition probabilities are investigated. The system under consideration is more general, which covers the systems with completely known and completely unknown transition probabilities as two special cases — the latter is hereby the switched linear systems under arbitrary switching. Moreover, in contrast with the uncertain transition probabilities studied recently, the concept of partly unknown transition probabilities proposed in this paper does not require any knowledge of the unknown elements. The sufficient conditions for stochastic stability and stabilization of the underlying systems are derived via LMIs formulation, and the relation between the stability criteria currently obtained for the usual MJLS and switched linear systems under arbitrary switching, are exposed by the proposed class of hybrid systems. Two numerical examples are given to show the validity and potential of the developed results.     

On reachable set synthesis of delay Markovian jump systems under partially delay-dependent asynchronous control

This paper pays close attention to the reachable set synthesis problem for discrete-time delayed Markovian jump systems (DDMJSs) under partially asynchronous control. Different from the traditional controller, a class of partially asynchronous controller is proposed, where delay-free and delay states are comprised and cannot take place at the same time. In addition, Bernoulli variable is used to describe the probability distribution of the above two kinds of states, and the design of feedback controller is considered. On this basis, the sufficient conditions which the state feedback controller is existent are solved effectively by using linear matrix inequalities (LMIs). Furthermore, the results of reachable set synthesis are extended to the DDMJs with uncertain transition probabilities. Finally, several numerical simulations are given to show the effectiveness of the presented methods.     

Anti-disturbance control for time-varying delay Markovian jump nonlinear systems with multiple disturbances

In this paper, the problem of composite anti-disturbance resilient control is addressed for time-varying delay Markovian jump nonlinear systems with multiple disturbances. The disturbances are assumed to include two parts: the first one in the input channel is described by an external system with perturbations; the second one is supposed to be bounded H₂ norm. By combining disturbance observer and L₂–L_∞ control method, the disturbances are attenuated and rejected, simultaneously, and the desired dynamic performance can be obtained for time-varying delay Markovian jump nonlinear systems. Moreover, the gains of the resilient controller and the observer are acquired by applying linear matrix inequalities (LMIs) technology. Finally, an application example is presented to show the effectiveness of the proposed approach.     

Passivity analysis and passification of uncertain Markovian jump systems with partially known transition rates and mode-dependent interval time-varying delays

In this paper, the problem of delay-dependent robust passivity analysis and robust passification of uncertain Markovian jump linear systems (MJLSs) with partially known transition rates and mode-dependent time-varying delays are investigated. In the deterministic model, the time-varying delay is in a given range and the uncertainties are assumed to be norm bounded. By constructing an appropriate Lyapunov–Krapunov functional (LKF) combining with Jensen’s inequality and the free-weighting matrix method, delay-dependent passification conditions are obtained in term of linear matrix inequalities(LMIs). For the robust passification problem, desired passification controllers are designed, which guarantee that the closed-loop MJLS is passive. Finally, a numerical example is given to illustrate the effectiveness of the proposed approach.     

Delay-dependent stability analysis for discrete-time singular Markovian jump systems with time-varying delay

This article considers the problem of delay-dependent stability analysis for a class of discrete-time singular systems with Markovian jump and time-varying delay. The transition probabilities in Markov chain are assumed to be partially unknown. In terms of linear matrix inequality approach, the delay-dependent criteria are proposed to ensure the underlying system to be regular, causal and stochastically stable. Several numerical examples are given to demonstrate the effectiveness and less conservatism of the obtained results.     

Improved exponential stability criteria for uncertain neutral system with nonlinear parameter perturbations

This paper investigates the problem of robust exponential stability for neutral systems with time-varying delays and nonlinear perturbations. Based on a novel Lyapunov functional approach and linear matrix inequality technique, a new delay-dependent stability condition is derived. Since the model transformation and bounding techniques for cross terms are avoided, the criteria proposed in this paper are less conservative than some previous approaches by using the free-weighting matrices. One numerical example is presented to illustrate the effectiveness of the proposed results.     

New stochastic robust stability criteria for time-varying delay neutral system with Markovian jump parameters

In this paper, the problem of stochastic robust stability of time-varying delay neutral system with Markovian jump parameters is investigated. The jumping parameters are considered as a continuous-time, continuous state Markov process. Based on the Lyapunov-Krasovskii functional approach, a new delay-dependent stochastic stability criteria is presented in terms of LMIs. A numerical example is given to illustrate the effectiveness of the developed method.     

Robustness of stability of nonlinear systems with stochastic delay perturbations

Suppose there exist random disturbances to a given exponentially stable system and the stochastically perturbed system is described by a stochastic differential-functional equation. In this paper a sufficient condition is given so that the perturbed system remains exponentially stable. In the case where the perturbation depends only on several states of the past we obtain a condition under which the perturbed system is absolutely exponentially stable.     

Markov 系统矩阵未知情况下的控制器设计

针对Markov 系统矩阵参数未知的实际情况, 提出一种基于状态反馈控制与自适应控制相结合的控制方法. 基于线性矩阵不等式技术给出相应控制器参数的求解条件. 与现有大多数自适应控制方法相比, 所提方法不仅使估计误差几乎处处有界, 而且原系统的系统状态几乎处处渐近稳定, 具有较好的收敛特性. 在所得结果的基础上, 进一步讨论了转移速率部分未知时的相关控制问题. 数值算例验证了所提出的设计方法的有效性.

     

Composite anti‐disturbance resilient control for Markovian jump nonlinear systems with partly unknown transition probabilities and multiple disturbances

In this paper, the problem of composite anti‐disturbance resilient control is studied for Markovian jump nonlinear systems with partly unknown transition probabilities and multiple disturbances. The multiple disturbances include two types: one is in the input channel generated by an exogenous system with perturbations, and the other is belong to L ₂[0,∞ ). The first class of disturbances is estimated by designing a disturbance observer. Combining the disturbance estimation with conventional L ₂ ? L _∞ resilient control law, a composite anti‐disturbance control scheme is constructed such that the closed‐loop system is stochastically stable, and different types of disturbances can be attenuated and rejected. By using Lyapunov function method and linear matrix inequalities technique, some sufficient conditions for the desired controller and observer gains are developed. Finally, an application example is provided to demonstrate the effectiveness of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.     

L 1 control for positive Markovian jump systems with partly known transition rates

International Journal of Control, Automation and Systems - This paper deals with the problem of L 1 control for positive Markovian jump systems with partly known transition rates. First, by...