随机非线性扰动下广义马氏跳变系统的控制器设计

针对实际系统中非线性扰动以一定概率存在的情况, 讨论广义马氏跳变系统的控制问题. 首先, 运用Bernoulli 变量描述系统中非线性扰动的存在与否, 建立相应的数学模型, 得到在上述一般条件下系统的随机容许性与解的存在唯一性条件. 然后, 以LMI 形式给出模态依赖和模态独立控制器的存在条件. 与现有结果相比, 所得结果考虑了非线性扰动的存在概率, 具有较小的保守性. 最后, 通过数值例子验证了所得结果的有效性和优越性.

     

马尔可夫信息物理系统拒绝服务攻击安全控制

研究了马尔可夫跳变信息物理系统(CPS)在模态依赖拒绝服务(Do S)攻击下的安全控制问题.提出了一种模态依赖事件触发策略来减少网络资源消耗.特别地,DoS攻击被设置为依赖系统模态,从而更贴近实际的应用.基于Lyapunov Krasovskii泛函方法建立了闭环系统在Do S攻击下渐近一致有界的充分性条件.更进一步,根据矩阵技术设计了所需的安全控制器.最后,通过一个实例说明了该方法的有效性.     

广义马尔科夫跳变系统的部分模态依赖观测器设计

针对系统状态变量不完全可测以及系统模态不能实时获得的实际情况,研究广义马尔科夫跳变系统的部分模态依赖观测器及相应控制器的设计问题.基于线性矩阵不等式技术,运用模态依赖的李雅普诺夫函数讨论广义马尔科夫系统的正则和无脉冲特性,给出使系统随机稳定的基于观测器的控制器存在的充分条件.最后通过数值算例验证了所提出设计方法的有效性和优越性.     

基于不完全转移率的连续Markov 跳变奇异系统的H∞ 控制

研究一类不完全转移率信息的Markov跳变奇异系统的H∞控制问题,提出连续Markov跳变奇异系统的新型有界实引理,并将其推广到不完全转移率条件.进一步设计H∞状态反馈控制器,使得闭环系统在转移率部分未知的条件下随机可容许,且满足H∞性能H.所得结论涵盖了奇异矩阵模态依赖情形,且表示为严格线性矩阵不等式形式,利于工程实现.最后,通过仿真算例表明了所提出方法的有效性和优越性.     

具有模态依赖时延的网络控制系统的H∞ 控制

针对一类模态依赖时延的网络控制系统,研究其H∞控制问题.基于马尔可夫跳变理论,通过构造随机的Lyapunov-Krasovskii函数,基于自由权重矩阵方法,得到H∞指标约束下闭环系统随机稳定的充分条件,并给出了马尔可夫模态依赖的状态反馈H∞控制器的设计方法.仿真实例验证了该设计方法的有效性.     

基于不完全转移率的连续Markov跳变奇异系统的Η∞控制

研究一类不完全转移率信息的Markov跳变奇异系统的Η∞控制问题,提出连续Markov跳变奇异系统的新型有界实引理,并将其推广到不完全转移率条件。进一步设计Η∞状态反馈控制器,使得闭环系统在转移率部分未知的条件下随机可容许,且满足Η∞性能γ。所得结论涵盖了奇异矩阵模态依赖情形,且表示为严格线性矩阵不等式形式,利于工程实现。最后,通过仿真算例表明了所提出方法的有效性和优越性。     

跳变双线性随机系统饱和执行器的镇定

对于一类具有Markov跳变参数的双线性离散随机系统,研究其饱和执行器问题.分别采用一般二次型Lyapunov函数、饱和关联Lyapunov函数进行系统随机稳定性分析,以椭圆不变集构造随机稳定域,提出两种依赖于模态跳变率的饱和状态控制器设计方法,两种方法均以线性矩阵不等式的形式给出.     

基于事件触发的马尔可夫跳变系统耗散性滤波

研究网络化马尔可夫跳变系统的耗散性滤波器设计问题。特别地，采用事件触发的通信策略，设计相应的具有耗散性能的模态依赖滤波器。通过使用Lyapunov-Krasovskii泛函方法，建立充分性条件以确保过滤误差系统能够满足给定的耗散性指标。分别根据线性矩阵不等式设计相应的模态依赖滤波器增益和事件触发参数。通过仿真实例验证了理论结果的有效性。     

一类连续广义Markov跳变系统的镇定性研究

研究转移概率部分未知情况下的连续时间广义Markov跳变系统的稳定性和镇定性.所研究的系统涵盖了转移概率完全已知和完全未知两种特殊情况,具有更广泛的意义.首先,基于线性矩阵不等式方法,获得了使系统正则、无脉冲、随机稳定的充分条件;然后,设计了基于线性矩阵不等式条件的状态反馈控制器,使闭环系统正则、无脉冲、随机稳定;最后,通过仿真算例验证了所提出方法的有效性.     

含参数不确定性的马尔可夫跳变过程鲁棒正实控制

讨论一类具有随机跳变参数的线性系统正实控制问题,其跳变参数的跃迁由有限状态的马尔可夫过程描述.基于随机李亚普诺夫函数的方法,并结合线性矩阵不等式,分别提出依赖于模态的状态反馈和输出反馈控制,以保证相应闭环系统的严格正实性.进一步针对系统含参数不确定性的情形,引入鲁棒正实性分析,得到鲁棒正实控制器存在的充分条件和设计方法.     

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.     

A Bounded Real Lemma for Discrete‐Time Markovian Jump Singular Systems

This paper presents a bounded real lemma for discrete‐time Markovian jump singular systems. First, a new necessary and sufficient condition is proposed in terms of a strict linear matrix inequality, which guarantees the stochastic admissibility of the unforced Markovian jump singular systems. Then, a bounded real lemma for discrete‐time Markovian jump singular systems is derived. It is also proven that the bounded real lemma can be described by a strict matrix inequality. Finally, a numerical example is provided to illustrate the effectiveness of the proposed theory. The results are more tractable and reliable in numerical computations than existing conditions.     

Robust stability and H-infinity control for uncertain discrete-time Markovian jump singular systems

The robust stability and stabilization, and H-infinity control problems for discrete-time Markovian jump singular systems with parameter uncertainties are discussed. Based on the restricted system equivalent （r.s.e.） transformation and by introducing new state vectors, the singular system is transformed into a discrete-time Markovian jump standard linear system, and the linear matrix inequality （LMI） conditions for the discrete-time Markovian jump singular systems to be regular, causal, stochastically stable, and stochastically stable with 7- disturbance attenuation are obtained, respectively. With these conditions, the robust state feedback stochastic stabilization problem and H-infinity control problem are solved, and the LMI conditions are obtained. A numerical example illustrates the effectiveness of the method given in the oaoer.     

Robust stability and H-infinity control for uncertain discrete-time Markovian jump singular systems

The robust stability and stabilization, and H-infinity control problems for discrete-time Markovian jump singular systems with parameter uncertainties are discussed. Based on the restricted system equivalent (r.s.e.) transformation and by introducing new state vectors, the singular system is transformed into a discrete-time Markovian jump standard linear system, and the linear matrix inequality (LMI) conditions for the discrete-time Markovian jump singular systems to be regular, causal, stochastically stable, and stochastically stable with °- disturbance attenuation are obtained, respectively. With these conditions, the robust state feedback stochastic stabilization problem and H-infinity control problem are solved, and the LMI conditions are obtained. A numerical example illustrates the effectiveness of the method given in the paper.     

Output feedback stabilization for discrete singular systems with random abrupt changes

The problem of static output feedback control is investigated for discrete singular systems with Markovian jump. Two necessary and sufficient conditions for the discrete singular Markovian jump system to be regular, causal and stochastically stable are proposed in terms of linear matrix inequality (LMI) approach. Two kinds of design methods of the desired mode‐independent static output feedback controller are given. The explicit expressions for the desired controller are also given. Numerical examples are proposed to show the validness of the developed results. Copyright © 2009 John Wiley & Sons, Ltd.     

Robust stabilization of singular markovian jump systems with uncertain switching

This paper focuses on the robust stabilization problem for a class of singular Markovian jump systems with uncertain switching probabilities. Based on a slack matrix method on transition probabilities, a new criterion for quadratically stochastic admissibility of such an uncertain system is established. Then, two new sufficient conditions for the existence of mode-dependent controller are given as linear matrix inequalities. Especially, a more practical controller named as mode-independent controller is derived by a mode-dependent Lyapunov function. Finally, a numerical example is used to demonstrate the effectiveness of the proposed methods.     

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 normalization and guaranteed cost control for a class of uncertain singular Markovian jump systems via hybrid impulsive control

This paper investigates the problem of robust normalization and guaranteed cost control for a class of uncertain singular Markovian jump systems. The uncertainties exhibit in both system matrices and transition rate matrix of the Markovian chain. A new impulsive and proportional‐derivative control strategy is presented, where the derivative gain is to make the closed‐loop system of the singular plant to be a normal one, and the impulsive control part is to make the value of the Lyapunov function does not increase at each time instant of the Markovian switching. A linearization approach via congruence transformations is proposed to solve the controller design problem. The cost function is minimized via solving an optimization problem under the designed control scheme. Finally, three examples (two numerical examples and an RC pulse divider circuit example) are provided to illustrate the effectiveness and applicability of the proposed methods. Copyright © 2013 John Wiley & Sons, Ltd.     

Sliding mode control of singular stochastic hybrid systems

This paper is concerned with the sliding mode control (SMC) of nonlinear singular stochastic systems with Markovian switching. An integral sliding surface function is designed, and the resulting sliding mode dynamics is a full-order Markovian jump singular stochastic system. By introducing some specified matrices, a new sufficient condition is proposed in terms of strict linear matrix inequality (LMI), which guarantees the stochastic stability of the sliding mode dynamics. Then, a SMC law is synthesized for reaching motion. Moreover, when there exists an external disturbance, the ?₂ disturbance attenuation performance is analyzed for the sliding mode dynamics. Some related sufficient conditions are also established.     

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.