一类不确定离散系统的严格正实分析和设计

考虑了一类不确定离散多变量系统严格正实分析和控制问题,其中不确定参数具有非负性.分析了系统鲁棒稳定且严格正实的条件,讨论了状态反馈、输出反馈使闭环系统鲁棒稳定且严格正实的问题.将不确定系统的鲁棒严格正实分析和设计转化为确定系统的严格正实分析和控制,得到了系统鲁棒稳定且严格正实的充分必要条件.最后给出了鲁棒严格正实控制问题的可解条件及控制器的综合方法.     

离散广义系统的鲁棒严格正实控制

研究确定的以及具有范数有界不确定性的离散广义系统的严格正实分析和控制问题,首先给出了确定离散广义系统状态反馈扩展严格正实控制器的存在条件和设计方法；然后利用线性矩阵不等式分析了不确定离散广义系统广义二次稳定且扩展严格正实的条件，讨论了状态反馈使闭环系统广义二次稳定且扩展严格正实问题，给出了状态反馈鲁棒扩展严格正实控制器的综合方法；最后通过数值算例说明了所提出方法的有效性．     

严格正实线性多变量系统的鲁棒性分析及其输出反馈控制

讨论一类线性不确定系统的鲁棒严格正实分析和控制问题，其中各不确定参数矩阵具有线性分式形式，分析了这类系统对所有容许不确定性严格正实的条件，并综合了使闭环内稳且严格正实的动态输出反馈控制器，通过适当地构造增广系统，将这类问题转化为确定系统的严格正实分析和设计，并按增广系统给出了这类不确定系统鲁棒严格正实的充分必要条件以及动态输出反馈鲁棒严格正实控制器的存在条件。     

一类不确定性系统的鲁棒正实性分析与综合

考虑一类具有多项式型不确定性系统的鲁棒正实性分析和综合问题。这类不确定模型是区间摄动和范数有界摄动系统的自然推广。给出了一个系统具有鲁棒扩展严格正实性 (ESPR)的充分条件 ,利用该条件可估计出使系统保持 ESPR的最大参数摄动范围。在 ESPR分析的基础上 ,进一步给出了ESPR控制器的存在条件和控制器的构造方法。通过凸优化算法 ,得到了所提出方法意义下具有最大摄动界的 ESPR控制器设计方法。     

一类参数不确定系统的鲁棒正实性

本文考虑了一类参数不确定系统的鲁棒正实性,给出了一个输出反馈系统具有鲁棒严格扩展正实性（ESPR）的充分条件以及求反馈控制器的方法。并利用该条件可估计出系统保持ESPR的最大参数撮动范围。在此基础上,对某不确定控制系统进行了鲁棒正实控制设计。并采用两种方法对结果进行验证,仿真的结果证明了该设计的有效性与可行性。     

参数摄动系统的鲁棒H ∞状态估计

基于Shaked提出的参数依赖型有界实引理，研究具有凸多面体参数摄动系统的鲁棒H∞状态估计问题．采用线性矩阵不等式技术，推导出此类不确定系统的全阶鲁棒H∞滤波器存在的充分条件，并将滤波器的设计转化为一个凸优化的求解问题．与传统的基于二次稳定的滤波方案相比，该滤波器设计方法具有较小的保守性．     

时延网络控制系统的模型预测控制

针对有输入约束的不确定时延网络控制系统,提出鲁棒模型预测控制方法;其中,将不确定时延建模为范数有界的输入矩阵的不确定性．给出了鲁棒性能指标的上界和系统渐近稳定的充分条件,通过在线求解LMI凸优化问题得到状态反馈控制律．仿真例子验证了该方法的有效性．     

离散时滞系统的鲁棒无源控制

1 引言在控制系统理论中正实理论起到了很大的作用, 引起了众多学者的关注[1～5]. 对这个问题的研究主要是出于鲁棒控制和非线性控制的需要. 在实际的工业生产过程中, 时滞与不确定现象是普遍存在的且时滞的引入大大增强了控制难度. 因此研究时滞系统的鲁棒正实控制具有一定的复杂性和难度. 文献[6]引入无源性概念, 研究了线性连续时滞系统的无源控制问题,但没有考虑模型的不确定性. 尽管离散时滞系统的无源控制与连续系统具有同等重要的地位, 但据作者所知, 目前尚未见相关报道. 本文考虑了一类时变不确定离散时滞系统的鲁棒无源控制问题, 提出了可将时滞系统的无源控制问题转化为分析一类非时滞离散确定系统的正实性. 基于LMI(Linear Matrix Inequality)研究了采用静态状态反馈和动态输出反馈情形下的鲁棒无源控制问题.     

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.     

不确定线性系统的输出反馈鲁棒H∞控制

研究了具有范数有界参数不确定线性系统的输出反馈鲁棒Ｈ∞控制问题，给出了该系统带Ｈ∞指标γ鲁棒稳定的充要条件，以及该系统静态输出反馈带Ｈ∞指标γ鲁棒镇定的充要条件，并且指出，系统的动态输出反馈鲁棒Ｈ∞镇定问题可等价为广义系统的静态输出反馈鲁棒Ｈ∞镇定问题，所给出的方法，其设计过程只需解一个特殊的Ｒｉｃｃａｔｉ方程最后通过实例论证了方法的有效性。     

Non-fragile positive real control for uncertain linear neutral delay systems

This paper is concerned with the problem of non-fragile positive real control for uncertain neutral delay systems with time-invariant norm-bounded parameter uncertainty. Time delays are assumed to appear in both the state and the controlled output equations. The state feedback gains are with norm-bounded controller uncertainties. For both the cases with additive and multiplicative controller uncertainties, we address the problem of designing memoryless state feedback controllers such that, for all admissible uncertainties, the resulting closed-loop system is stable and the closed-loop transfer function is extended strictly positive real. Sufficient conditions for the existence of desired controllers are given in terms of linear matrix inequalities (LMIs). When these LMIs are feasible, the expected memoryless state feedback controller can be easily constructed via convex optimization. An illustrative example is given to demonstrate the validity and applicability of the proposed approach.     

Positive real control problem for uncertain linear time-invariant systems

This paper focuses on positive real control of linear time-invariant systems which are subjected to norm-bounded uncertainties in the state equation. We address the problem of designing a linear dynamic output feedback controller that robustly stabilizes the uncertain system and achieves the extended strict positive realness property for a given closed-loop transfer function. It is shown that a solution to the above problem can be obtained by solving a scaled strict positive real control problem for which no parameter uncertainty occurs.     

Robust H/sub /spl infin// control for fuzzy systems with Frobenius norm-bounded uncertainties

In this paper, we investigate the problem of robust H/sub /spl infin// performance and stabilization for a class of uncertain fuzzy systems with Frobenius norm-bounded parameter uncertainties in all system matrices. Both continuous- and discrete-time uncertain fuzzy systems are considered under a unified treatment called bounded real lemma for fuzzy systems. Unlike the bounded real lemma in the linear theory of robust H/sub /spl infin// control where necessary and sufficient conditions were obtained, only sufficient condition based on Lyapunov method is shown. Furthermore, connection between robust H/sub /spl infin// problems involving uncertainty and standard uncertainty-free H/sub /spl infin// problems is established via matrix algebra. As for controller synthesis, a state feedback fuzzy control law is designed via relaxed linear matrix inequality (LMI) formulations.     

Robust analysis and synthesis for a class of uncertain nonlinear systems with multiple equilibria

This paper focuses on a class of uncertain nonlinear systems which are subject to norm-bounded parameter uncertainty in the forward path and a vector-valued periodic nonlinearity in the feedback path, and addresses robust analysis and synthesis problems for such systems. Sufficient conditions for global asymptotic stability are derived in terms of linear matrix inequalities (LMIs) and a technique for the estimation of the uncertainty bound is proposed by solving a generalized eigenvalue minimization problem. The problem of robust synthesis is concerned with designing a feedback controller such that the resulting closed-loop system is globally asymptotically stable for all admissible uncertainties. It is shown that a solution to the robust synthesis problem for the uncertain system can be obtained by solving a synthesis problem for an uncertainty free system. A concrete example is presented to demonstrate the applicability and validity of the proposed approach.     

An algebraic approach to the robust stability analysis and robust stabilization of uncertain singular systems

This paper considers the problems of robust stability analysis and robust stabilization for uncertain singular systems with norm-bounded time-varying uncertainties. The robust stability problem is solved via the notion of generalized quadratic stability which guarantees that the uncertain singular system is stable, regular and impulse free simultaneously for all admissible uncertainties, while the robust stabilization problem is solved via the notion of generalized quadratic stabilizability. An algebraic approach is adopted in the paper. Our main results are extensions of some existing results on uncertain regular systems for singular systems.