离散区间系统的二次稳定性及其稳定裕度分析

研究了动态离散区间系统的鲁棒稳定性问题,提出了系统二次稳定的充分与必要条件,以及相应的稳定裕度的计算方法,并推广到离散参数不确定系统.所有结论以线性矩阵不等式(LMI)的形式给出.利用功能强大的LMI工具,求解非常方便.所给实例表明,该方法用于确定动态离散区间系统的鲁棒稳定性及其稳定裕度,非常有效.     

Robust ISS of uncertain discrete-time singularly perturbed systems with disturbances

This paper is concerned with robustly input-to-state stable (ISS) and Robust ISS by feedback of uncertain discrete-time singularly perturbed systems (SPSs) with disturbances. Meanwhile, robust stability and stabilisation of uncertain discrete-time SPSs are also obtained as the particular cases of robust ISS and robust ISS by feedback. We first find a sufficient condition by using the fixed-point principle in terms of linear matrix inequalities (LMIs) to guarantee that the considered system is always standard discrete-time SPSs subject to uncertainty and disturbances. Then, the full systems could decompose into the continuous-time uncertain slow subsystem with disturbance and discrete-time uncertain fast subsystems with disturbance, respectively. Based on the two-time-scale decomposition technique, sufficient condition in terms of LMIs is given such that the full systems are uniformly standard and robust ISS simultaneously. In addition, a state feedback controller is constructed by using the LMI approach such that the resulting closed-loop systems are robust ISS. Finally, a numerical example is provided to illustrate the effectiveness of the proposed approach.     

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．     

An LMI condition for the robust stability of uncertaincontinuous-time linear systems

A new sufficient condition for the robust stability of continuous-time uncertain linear systems with convex bounded uncertainties is proposed in this note. The results are based on linear matrix inequalities (LMIs) formulated at the vertices of the uncertainty polytope, which provide a parameter dependent Lyapunov function that assures the stability of any matrix inside the uncertainty domain. With the aid of numerical procedures based on unidimensional search and the LMIs feasibility tests, a simple and constructive way to compute robust stability domains can be established     

不确定多通道奇异时滞系统分散H∞控制

针对不确定多通道奇异时滞大系统, 研究其分散鲁棒H_∞控制问题. 假定不确定性是时不变、范数有界. 基于奇异系统Lyapunov稳定性理论, 通过设定Lyapunov-Krasovskii矩阵为合适的块对角结构, 推导出了使不确定多通道奇异时滞大系统可鲁棒镇定, 且满足一定的扰动水平的充分条件即一组线性矩阵不等式(LMIs)有可行解. 给出了具有期望阶数的分散输出反馈H_∞控制器的设计方法.     

一类不确定系统的鲁棒稳定性分析

研究了一类不确定系统的稳定性问题, 以线性矩阵不等式(LMI)的形式给出了该类系统的鲁棒稳定条件, 并将该结果推广到区间系统的稳定性分析, 提出了研究区间系统稳定性问题的新方法, 给出了线性矩阵不等式形式的稳定判据, 该判据将区间系统的稳定性问题转化为一类线性矩阵不等式的可解问题. 最后通过仿真算例验证了本文结果具有更小的保守性.     

Improved exponential estimates for neutral systems

Improved exponential estimates and a new sufficient condition for the exponential stability of neutral type time‐delay systems are established in terms of linear matrix inequalities (LMIs). A new Lyapunov‐Krasovskii functional candidate with appropriately constructed exponential terms is introduced to prove the exponential stability and to reduce the conservatism. For the uncertain case, a corresponding condition for the robust exponential stability is also given. It is shown by numerical examples that the proposed conditions are less conservative than existing results. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Stabilization of a class of uncertain time-delay systems containing saturating actuators

The delay-dependent robust stabilization problem for a class of uncertain linear timedelay systems containing saturating actuator is considered in this paper. The uncertain time-delay systems under consideration are described by state differential equations with time-varying unknown-but-bounded uncertain parameters and delayed state. The delay is assumed to be constant bounded but unknown. New robust stability criteria and a sufficient condition for the existence of memoryless robust stabilizing control law are derived. The results depend on the size of the delay and are given in terms of several linear matrix inequalities (LMIs). A numerical example is presented to illustrate the obtained results.     

Robustness of interval gene networks with multiple time-varying delays and noise

In this paper, we investigate the problem how to establish the robust stability of uncertain gene networks with time-varying delays and noise. Specifically, we consider uncertain gene networks where the regulation occurs at the mRNAs level, and we obtain a sufficient condition for robust stability by Lyapunov method and inequality technique. Moreover, we show that these condition can be formulated as linear matrix inequalities (LMIs), which are easy to be verified by the convex optimization. Finally, two of the most common motifs are investigated to illustrate the effectiveness and the correctness of our results.     

Delay dependent robust stability of singular systems with additive time-varying delays

This paper considers the problem of delay-dependent robust stability for uncertain singular systems with additive time-varying delays. The purpose of the robust stability problem is to give conditions such that the uncertain singular system is regular, impulse free, and stable for all admissible uncertainties. The results are expressed in terms of linear matrix inequalities (LMIs). Finally, two numerical examples are provided to illustrate the effectiveness of the proposed method.     

时变时滞不确定系统的鲁棒输出反馈控制

研究了时变时滞不确定系统基于状态观测器的动态输出反馈实现鲁棒镇定的分 析和综合问题.所研究的系统不仅同时包含时变状态时滞和时变控制时滞,而且包含时变未 知且有界不确定参数.提出了确保该系统可通过输出反馈鲁棒镇定的充分条件,并将该充分 条件转化为线性矩阵不等式(LMI)问题,最终通过求解两个LMI来构造输出反馈控制律.     

带饱和执行器的不确定时滞系统的鲁棒控制

研究了一类具有饱和执行器约束的不确定时滞系统时滞依赖型无记忆鲁棒控制问 题.所考虑的时滞系统包括时变未知但有界的不确定参数以及状态和控制的时滞项.文中应 用了Lyapunov定理以及线性矩阵不等式(LMI)方法来研究该系统的分析和综合问题,导出 了一个新的鲁棒可镇定判据和相应的无记忆鲁棒镇定控制律设计方法.所得的基于一组 LMIs的结果是与时滞相关的.     

On absolute stability of Lur''''e control systems with multiple non-linearities using linear matrix inequalities

Necessary and suffcient conditions for the existence of a Lyapunov function in the Lur'e form to guarantee the absolute stability of Lur'e control systems with multiple non-linearities are discussed in this paper. It simplifies the existence problem to one of solving a set of linear matrix inequalities (LMIs), If those LMIs are feasible, free parameters in the Lyapunov function,such as the positive definite matrix and the coefficients of the integral terms, are given by the solution of the LMIs. Otherwise, this Lyapunov function does not exist. Some sufficient conditions are also obtained for the robust absolute stability of uncertain systems.A numerical example is provided to demonstrate the effectiveness of the proposed method.     

On absolute stability of Lur＇e control systems with multiple non-linearities using linear matrix inequalities

Necessary and suffcient conditions for the existence of a Lyapunov function in the Lur‘e form to guarantee the absolute stability of Lur‘e control systems with multiple non-linearities are discussed in this paper. It simplifies the existence problem to one of solving a set of linear matrix inequalities (LMIs). If those LMIs are feasible, free parameters in the Lyapunov function, such as the positive definite matrix and the coefficients of the integral terms, are given by the solution of the LMIs. Otherwise, this Lyaptmov function does not exist. Some sufficient conditions are also obtained for the robust absolute stability of uncertain systems. A numerical example is provided to demonstrate the effectiveness of the proposed method.     

一类具有非线性饱和执行器的不确定时滞系统鲁棒控制

研究一类具有非线笥饱和执行器朱确定线性时滞系统的鲁棒性镇定问题。所考虑的不确定时滞系统具有时变未知且有界的不确定参数和状态时滞。提出了新的鲁棒可镇定判据和相应的鲁棒无记忆状态反馈控制器设计方法。数值仿真例子说明了所提出方法的有效性。     

参数不确定性广义周期时变系统的鲁棒稳定性分析

基于广义周期时变系统允许的充分必要条件,提出了参数不确定性广义周期时交系统鲁棒稳定的概念,并得到了该类系统鲁棒稳定的充分必要条件．研究在状态反馈控制下保证闭环系统鲁棒稳定的条件,给出了一族状态反馈鲁棒稳定器的设计方法．引入广义周期时变系统二次稳定的概念,讨论了二次稳定性与鲁棒稳定性的关系．最后通过数值算例说明了所得的主要结果,     

带饱和执行器的不确定时滞系统的 鲁棒控制

研究了一类具有饱和执行器约束的不确定时滞系统时滞依赖型无记忆鲁棒控制问题 .所考虑的时滞系统包括时变未知但有界的不确定参数以及状态和控制的时滞项 .文中应用了 Lyapunov定理以及线性矩阵不等式 ( LMI)方法来研究该系统的分析和综合问题 ,导出了一个新的鲁棒可镇定判据和相应的无记忆鲁棒镇定控制律设计方法 .所得的基于一组LMIs的结果是与时滞相关的     

不确定状态滞后线性跳跃系统的时滞相关鲁棒非脆弱H∞控制

讨论了一类具有Markov跳跃参数的不确定混合线性时滞系统的鲁棒非脆弱控制问题.给出了使系统鲁棒随机稳定并具有给定的H∞性能的充分条件.并且通过参数变换和Schur补定理,将已得出的充分条件转化成一系列耦合的线性矩阵不等式形式以便于控制器参数的求解.仿真结果表明了本文提出的鲁棒非脆弱控制方法的有效性.     

基于线性矩阵不等式的不确定关联系统的分散鲁棒镇定

应用线性矩阵不等式（LMI）方法研究不确定性关联大系统的分散便棒镇定问题。系统中不稳定项具有数值界,可不满足匹配条件。基于不确定项的表达形式,给出了其可分散状态反馈镇定的充分条件,即一组LMIs有解。在此基础上,通过求第一凸优化问题,提出了具有较小反馈增益的分散稳定化状态反馈控制律的设计方法。仿真示例说明了该方法的有效性和优越性。