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.

     

Robust decentralized stabilization of Markovian jump large-scale systems: A neighboring mode dependent control approach

This paper is concerned with the decentralized stabilization problem for a class of uncertain large-scale systems with Markovian jump parameters. The controllers use local subsystem states and neighboring mode information to generate local control inputs. A sufficient condition involving rank constrained linear matrix inequalities is proposed for the design of such controllers. A numerical example is given to illustrate the developed theory.     

Stabilization of discrete-time Markovian jump linear systems via time-delayed controllers

This paper is concerned with the stabilization problem for a class of discrete-time Markovian jump linear systems with time-delays both in the system state and in the mode signal. The delay in the system state may be time-varying. The delay in the mode signal is manifested as a constant mismatch of the modes between the controller and the system. We first show that the resulting closed-loop system is a time-varying delayed Markovian jump linear system with extended state space. Then a sufficient condition is proposed for the design of a controller such that the closed-loop system is stochastically stable. Finally, numerical simulation is used to illustrate the developed theory.     

H∞ control for discrete‐time Markovian jump systems with partial information on transition probabilities

This paper focuses on mode‐dependent H_∞ state‐feedback control for a class of discrete‐time Markovian jump systems (MJSs) with partial information on transition probabilities (TPs). The augmented free‐connection weighting matrices are introduced by considering the influence of partial information of TPs on discrete‐time MJSs and the disturbance input on the state vector. As a result, the less conservative stability criterion and bounded real lemma (BRL) of MJSs with partly unknown TPs are obtained. Then the sufficient conditions for designing the mode‐dependent H_∞ controllers are derived in terms of linear matrix inequalities (LMIs). Numerical examples are given to illustrate the effectiveness and the merits of the proposed method.     

Quantized robust H-two filtering for Markovian jump linear systems over networks with nonaccessible mode information

This paper is concerned with the problems of H-two filtering for discrete-time Markovian jump linear systems subject to logarithmic quantization. We assume that only the output of the system is available, and therefore the mode information is nonaccessible. In this paper, a mode-independent quantized H-two filter is designed such that filter error system is stochastically stable. To this end, sufficient conditions for the existence of an upper bound of H-two norm are presented in terms of linear matrix inequalities. Considering uncertainty of system matrices, a robust H-two filter is designed. The proposed method is also applicable to cover the case where the transition probability matrix is not exactly known but belongs to a given polytope. Finally, numerical examples are provided to demonstrate the effectiveness of the proposed approach.     

Further results on finite-time stabilisation for stochastic Markovian jump systems with time-varying delay

In this paper, we study the issue of finite-time stabilisation for stochastic Markovian jump systems with time-varying delay by considering a new criterion on finite-time stability. By constructing more appropriate Lyapunov–Krasovskii functional, some new conditions for verifying the finite-time stability of the plant as well as controller synthesis are established in standard linear matrix inequalities. The practical example about a single-link robot arm model demonstrates the validity of the main results.     

Stability analysis of Markovian jump systems with delayed impulses

This paper addresses stability for Markovian jump systems with delayed impulses. The delayed impulse has a largely negative effect on the system stability and is not easy to be studied. The main reason is that so many factors such as Markovian switching, impulse, and time-varying delay are simultaneously contained and make its analysis complicated and difficult. In order to analyze these factors clearly, some novel enlarging techniques are presented and used to establish linear matrix inequality (LMI) conditions ultimately. Based on the given methods, more situations such as impulsive instant sequence satisfying a renewal process and Poisson process, respectively, are further studied and better than ones without considering such properties. Two numerical examples are used to show the effectiveness and superiority of the methods.     

转移概率部分未知的时滞不确定Markov跳跃系统稳定性分析

本文研究转移概率部分未知的时滞不确定的Markov 跳跃系统随机稳定性问题,基于Lyapunov稳定理论,构造合适的Lyapunov泛函,使用自由权矩阵技术和凸结合技术来估计积分项的上界,同时也充分考虑时滞下界和上界的关系,得到保证Markov 跳跃系统随机稳定性的充分性条件,该条件以线性矩阵不等式的形式表出。最后,一个数值例子和其仿真验证了我们所提方法的有效性和优越性。     

模型相关时变时滞马尔可夫跳变系统低保守稳定性

本文研究了时变时滞与模型相关的随机马尔可夫跳变系统的时滞相关稳定性问题. 通过建立时变时滞与模型相关的系统模型, 构造不同的Lyapunov-Krasovskii函数, 并通过引入改进的积分等式, 以线性矩阵不等式的形式提出了具有较小保守性的时滞依赖稳定性条件. 最后用几个数值算例说明本文结论的有效性及较低的保守性.     

On robust stabilization of Markovian jump systems with uncertain switching probabilities

This brief paper is concerned with the robust stabilization problem for a class of Markovian jump linear systems with uncertain switching probabilities. The uncertain Markovian jump system under consideration involves parameter uncertainties both in the system matrices and in the mode transition rate matrix. First, a new criterion for testing the robust stability of such systems is established in terms of linear matrix inequalities. Then, a sufficient condition is proposed for the design of robust state-feedback controllers. A globally convergent algorithm involving convex optimization is also presented to help construct such controllers effectively. Finally, a numerical simulation is used to illustrate the developed theory.     

Robust H∞ control of Markovian jump systems with uncertain switching probabilities

This paper is concerned with the robust H_∞ control problem for a class of Markovian jump systems with uncertain switching probabilities, whose uncertainties are assumed to be elementwise bounded. First, new criterion of H_∞ performance for such uncertain systems is given. Then, new sufficient condition for H_∞ controller is established as strict linear matrix inequalities. Finally, a numerical example is used to demonstrate the effectiveness of the proposed methods. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

A stability and contractiveness analysis of discrete-time Markovian jump linear systems

We propose performance criteria for discrete-time linear systems with Markov jumping parameters. Exact convex conditions for internal stability and contractiveness of such systems are expressed in terms of linear matrix inequalities. These conditions are of the same form as that in the Kalman-Yacubovich-Popov lemma.     

Stabilization of discrete‐time singular Markovian jump repeated vector nonlinear systems

This paper studies the control problem for discrete‐time singular Markovian jump systems with repeated vector nonlinearities. Sufficient conditions for stochastic stability are established, where the uniqueness of solution to the underlying system is also guaranteed. Then, a series of formulations of stabilizing conditions is further developed to design mode‐dependent and mode‐independent controllers by using the linear matrix inequality approach. Based on the proposed results, more special cases for stabilizing controller are considered. Finally, numerical examples are used to demonstrate the effectiveness and superiority of the proposed methods. Copyright © 2015 John Wiley & Sons, Ltd.     

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.     

Robust H-infinity filter design for uncertain time-delay singular stochastic systems with Markovian jump

This paper deals with the problem of H-infinity filter design for uncertain time-delay singular stochastic systems with Markovian jump. Based on the extended It^o stochastic differential formula, sufficient conditions for the solvability of these problems are obtained. Furthermore, It is shown that a desired filter can be constructed by solving a set of linear matrix inequalities. Finally, a simulation example is given to demonstrate the effectiveness of the proposed method.     

Robust H-infinity filter design for uncertain time-delay singular stochastic systems with Markovian jump

This paper deals with the problem of H-infinity filter design for uncertain time-delay singular stochastic systems with Markovian jump. Based on the extended It^o stochastic differential formula, sufficient conditions for the solvability of these problems are obtained. Furthermore, It is shown that a desired filter can be constructed by solving a set of linear matrix inequalities. Finally, a simulation example is given to demonstrate the effectiveness of the proposed method.     

New results on stabilization of Markovian jump systems with time delay

This paper studies the problem of stochastic stabilization for a class of Markovian jump systems with time delay. A new delay-dependent stochastic stability criterion on the stochastic stability of the system is derived based on a novel Lyapunov-Krasovskii functional (LKF) approach. The equivalence and superiority to existing results are demonstrated. Then a state feedback controller, which guarantees the stochastic stability of the closed-loop system, is designed. Illustrative examples are provided to show the reduced conservatism and effectiveness of the proposed techniques.     

Further improvement of stability criterion and BRL for Markovian jump systems with interval time-varying delay

This paper deals with delay-dependent stochastic stability and bounded real lemma(BRL)for Markovian jump linear systems with interval time-varying delays.By constructing some new Lyapunov functionals and using the Jensen’s integral inequality method,the free weighting matrix method,the convex combination method and the delay decomposition approach integratedly,some less conservative delay-dependent stability criteria and BRL are established. Numerical examples are given to show the effectiveness of the proposed method.