广义马氏跳变系统在一般转移速率下的控制器设计

针对转移概率不能精确获得并且部分未知的广义马氏跳变系统, 分别讨论在模态依赖控制器和模态独立控制器条件下的系统镇定问题. 与现有结果相比, 所提研究方法具有较小的保守性, 能够有效地解决实际问题. 首先, 运用自由权矩阵方法, 得到了广义马氏跳变系统在转移速率满足上述一般条件时系统随机容许的充分条件. 在此基础上, 以线性矩阵不等式(Linear matrix inequality, LMI)的形式分别给出了模态依赖和模态独立控制器的求解条件. 最后, 通过数值算例验证设计方法的有效性和优越性.     

有界丢包网络控制系统的稳定性与能稳性

主要讨论有界丢包网络控制系统的稳定性与能稳性. 基于迭代方法将有界丢包网络控制系统建模为一个跳变系统. 由于网络的复杂性, 跳变系统状态转移矩阵的部分元素无法获得, 因此, 我们考虑的这种情况更具有一般性. 并且本文考虑的丢包同时存在于前馈和反馈通道. 最后, 数值例子表明本文方法的有效性.     

Exponential stability of stochastic singular delay systems with general Markovian switchings

In recent years, Markovian jump systems have received much attention. However, there are very few results on the stability of stochastic singular systems with Markovian switching. In this paper, the discussed system is the stochastic singular delay system with general transition rate matrix in terms of uncertain and partially unknown transition rate matrix. The aim is to answer the question whether there are conditions guaranteeing the underlying system having a unique solution and being exponentially admissible simultaneously. The proposed results show that all the features of the underlying system such as time delay, diffusion, and general Markovian switchings play important roles in the system analysis of exponential admissibility. A numerical example is used to demonstrate the effectiveness of the proposed methods. Copyright © 2014 John Wiley & Sons, Ltd.     

Robust stability of Markovian jump discrete-time neural networks with partly unknown transition probabilities and mixed mode-dependent delays

This article discusses the robust stability problem for a class of uncertain Markovian jump discrete-time neural networks with partly unknown transition probabilities and mixed mode-dependent time delays. The transition probabilities of the mode jumps are considered to be partly unknown, which relax the traditional assumption in Markovian jump systems that all of them must be completely known a priori. The mixed time delays consist of both discrete and distributed delays that are dependent on the Markovian jump modes. By employing the Lyapunov functional and linear matrix inequality approach, some sufficient criteria are derived for the robust stability of the underlying systems. A numerical example is exploited to illustrate the developed theory.     

Stability analysis and stabilization of Markovian jump systems with time‐varying delay and uncertain transition information

The paper investigates the problems of stability and stabilization of Markovian jump systems with time‐varying delays and uncertain transition rates matrix. First, the stochastic scaled small‐gain theorem is introduced to analyze the stability of the Markovian jump system. Then, a new stability criterion is proposed by using a new Lyapunov‐Krasovskii functional combined with Wirtinger‐based integral inequality. The proposed stability condition is demonstrated to be less conservative than other existing results. The merit of the proposed approach lies in its reduced conservatism, which is made possible by a new precise triangle inequality and a new Lyapunov‐Krasovskii functional. Moreover, a controller design criterion is presented according to the stability criterion. Furthermore, the transition rate matrix is treated as partially known and with uncertainty, and the relevant stability and stabilization criteria are proposed. Finally, 3 numerical examples are provided to illustrate the superior result of the stability criteria and the effectiveness of the proposed controller design method.     

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.     

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.

     

具有双边随机时延和丢包的网络控制系统稳定性分析

针对具有双边随机网络时延和丢包的网络控制系统,首先基于Markov的随机过程描述系统丢包的特性;然后利用系统增广矩阵的方法建立参数不确定的离散时间跳变系统模型,在考虑Markov链转移概率矩阵中部分元素未知甚至完全未知的条件下,采用Lyapunov稳定理论和随机理论的分析方法,设计依赖于丢包特性且满足系统均方稳定要求的时变控制器;最后通过数值算例仿真表明所提出方法的有效性.     

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.     

Joint decision and control strategy for a class of nonhomogeneous Markovian jump systems with input constraints

This paper is concerned with the joint decision and control strategy for a class of nonhomogeneous Markovian jump systems subject to input constraints. By assuming the mode transition rate matrix (MTRM) of Markovian jump systems is piecewise homogeneous instead of homogeneous, a higher-level Markov chain represented by the higher-level mode transition rate matrix (HMTRM) is introduced to describe the variation of MTRM. Based on this, taking into account the minimization of system cost, a novel joint decision and control strategy is proposed in the presence of input constraints. This strategy consists of two sections: decisions are applied to the HMTRM such that the occurrence probability of subsystems is adjusted ultimately; next on the basis of altered HMTRM, controller is designed in view of input constraints. In comparison with conventional control method, this strategy not only guarantees the stability of the considered system well, but also decreases the system cost effectively. Numeral examples along with comparisons are put forward to illustrate the effectiveness of the proposed strategy.