一类含有输入时滞的不确定切换系统的鲁棒指数镇定

针对一类含有输入时滞的不确定切换系统,讨论了鲁棒指数镇定问题,提出了可行的切换控制器和切换信号的设计方法．首先,运用还原法将具有时滞的切换系统转化为无时滞的切换系统;然后,基于线性矩阵不等式,给出了系统在切换控制器和切换信号作用下鲁棒指数可镇定的充分条件,并利用多Ｌｙａｐｕｎｏｖ函数方法给出了定理的详细证明;最后,利用数值仿真例子验证了该方法的有效性．     

不确定多时滞离散切换系统的输出反馈镇定

针对一类具有多重状态时滞和凸多面体不确定性的离散切换系统,研究该系统在任意切换信号下基于状态观测器的输出反馈鲁棒镇定问题.首先通过状态变量的替换将多时滞项转变成不含时滞项,再利用分段Lyapunov函数和线性矩阵不等式方法,导出凸多面体不确定多时滞离散切换系统基于观测器的输出反馈鲁棒镇定的充分条件,并将此条件转化成为一组线性矩阵不等式的可行性问题,同时给出基于状态观测器的输出反馈控制器.仿真结果表明设计方法是可行有效的.     

一类含有输入时滞的不确定切换系统的鲁棒指数镇定

针对一类含有输入时滞的不确定切换系统,讨论了鲁棒指数镇定问题,提出了可行的切换控制器和切换信号的设计方法．首先,运用还原法将具有时滞的切换系统转化为无时滞的切换系统;然后,基于线性矩阵不等式,给出了系统在切换控制器和切换信号作用下鲁棒指数可镇定的充分条件,并利用多Ｌｙａｐｕｎｏｖ函数方法给出了定理的详细证明;最后,利用数值仿真例子验证了该方法的有效性．

     

异步时滞切换正系统的有限时间镇定

研究异步切换下时滞切换正系统的有限时间控制问题,即针对控制器切换滞后于子系统切换形成的异步现象,基于平均驻留时间切换方法对切换正系统开展有限时间镇定研究.首先,将每个正子系统运行的区间划分为子系统与控制器匹配和失配区间,并构造多余正Lyapunov-Krasovskii泛函;其次,基于有限时间稳定理论,实现平均驻留时间切换律及异步时滞切换正系统有限时间镇定控制器的联合设计,并给出连续时间和离散时间两种情形下系统有限时间镇定的充分条件;最后,通过两个仿真例子验证所提出方法的有效性.     

模糊不确定时滞系统的静态输出的反馈镇定:迭代线性矩阵不等式方法

对一类不确定非线性时滞系统利用模糊T＿S模型进行建模,研究了静态输出反馈镇定问题.用矩阵不等式的形式给出了模糊T＿S不确定时滞系统可通过静态输出反馈镇定的充分条件.并将矩阵不等式的条件转化为迭代线性矩阵不等式(ILMI),并给出相应的算法.     

时滞切换不确定神经网络系统的指数稳定性

本文研究了具有无穷时滞切换不确定细胞神经网络(UCNNs)系统任意切换下的指数稳定性.利用同胚映射和M-矩阵理论,得到UCNNs系统平衡点存在性,唯一性和指数稳定性的充分条件;利用Lyapunov泛函方法,研究了时滞切换UCNNs系统任意切换下的鲁棒指数稳定性,并得到确保系统全局指数稳定的充分条件.     

切换非线性系统的分布式模型预测控制

针对一类具有预先指定切换序列的切换非线性系统,研究了具有通信信道干扰和时滞测量的分布式模型预测控制问题.在每个子系统都存在镇定控制器的假设下,利用基于Lyapunov函数的模型预测控制器设计了分布式模型预测控制器,并给出了闭环切换非线性系统最终有界的充分条件.最后,通过仿真结果表明了分布式模型预测控制策略的有效性.     

多个线性时滞系统的关联稳定与协调控制

研究线性时滞系统的时滞无关关联稳定性和协调控制问题.利用双线性矩阵不等式(BMI),给出了两个系统关联稳定和协调镇定的充分条件,将关联和协调控制器的设计问题转化为具有BMI约束的非凸优化问题,并给出了求解这类问题的交替算法.最后,通过一个数值例子来说明本文结果的有效性.研究结果表明,不稳定的时滞系统可以通过设计关联或协调控制构成稳定的组合系统.     

一类单输入线性切换系统的可镇定性研究

考虑一类单输入线性切换系统的可镇定性问题，利用变结构控制对系统进行降维．通过对系统滑动模态的研究，得出了系统一致可镇定的充分条件和系统存在容许镇定策略的充分条件．给出了具体的容许镇定策略集合，并对二阶切换系统给出了详细的容许镇定策略．仿真实例验证了所提出结论的有效性．     

线性区间离散时滞系统的区域镇定

针对线性离散时滞系统的区域镇定问题, 基于非奇异状态变换技术提出了区间不确定性系统区域可镇定的充分条件, 保证闭环系统的所有极点均位于给定的圆盘区域内. 所给条件可简化为LMI描述形式, 利用LMI工具求解非常方便. 所给实例表明了该方法用于判断线性区间离散时滞系统的区域可镇定性与设计区域镇定控制器的可行性.     

线性系统时滞反馈镇定研究

本文研究线性系统状态反馈控制存在延迟时的镇定问题.对于一般情形下的时滞镇定问 题的判定,提出了一个充分条件;对于具有不稳定单根的单输入控制系统,提出了时滞镇定一 个构造性的充分条件;并讨论了时滞反馈镇定控制器的实现问题.     

Stability and Stabilizability of Switched Linear Systems: A Survey of Recent Results

During the past several years, there have been increasing research activities in the field of stability analysis and switching stabilization for switched systems. This paper aims to briefly survey recent results in this field. First, the stability analysis for switched systems is reviewed. We focus on the stability analysis for switched linear systems under arbitrary switching, and we highlight necessary and sufficient conditions for asymptotic stability. After a brief review of the stability analysis under restricted switching and the multiple Lyapunov function theory, the switching stabilization problem is studied, and a variety of switching stabilization methods found in the literature are outlined. Then the switching stabilizability problem is investigated, that is under what condition it is possible to stabilize a switched system by properly designing switching control laws. Note that the switching stabilizability problem has been one of the most elusive problems in the switched systems literature. A necessary and sufficient condition for asymptotic stabilizability of switched linear systems is described here.      

Memoryless stabilization of uncertain linear systems includingtime-varying state delays

The problem of stabilizing a class of uncertain time-delay systems via memoryless linear feedback is examined. The systems under consideration are linear systems with time-varying state delays. They also contain uncertain parameters (possibly time-varying) whose values are known only to within a prescribed compact bounding set. The main contribution given is to enlarge the class of time-delay systems for which one can construct a stabilizing memoryless linear feedback controller. Within this framework, a novel notion of robust memoryless stabilizability is first introduced via the method of Lyapunov functionals. Then a sufficient condition for the stabilizability is proposed. It is shown that solvability of a parameterized Riccati equation can be used to determine whether the time-delay system satisfies the sufficient condition. If there exists a positive definite symmetric solution satisfying the Riccati equation, a suitable memoryless linear feedback law can be derived     

Robust stabilization for non-linear discrete-time systems

This paper deals with the problem of robust stabilization for linear discrete-time systems under non-linear perturbations. Without limitation to single-input systems and restriction on the structures of both the positive definite matrix and the corresponding variable, a new sufficient condition is presented which guarantees the stability of the closed-loop system and at the same time maximizes the bound on the non-linearity. In addition, our main result is extended to discrete time-delay systems. All the conditions are given within the framework of linear matrix inequalities. The effectiveness of the methods is illustrated with three examples.     

Consensus in multi-agent systems with random delays governed by a Markov chain

This paper investigates the consensus problem in a multi-agent system with random delays governed by a Markov chain. The communication topology is assumed to be directed and fixed. With first-order dynamics under the sampled-data setting, we first convert the original system into a reduced-order one featuring the error dynamics. Accordingly, the consensus problem is transformed into the stabilization of the error dynamic system. Thereafter, based on the theory in stochastic stability for time-delay systems, a sufficient condition is established in terms of a set of linear matrix inequalities (LMIs). The mean square stability of the error dynamics is shown to guarantee consensus of the multi-agent system. By explicitly incorporating the transition probability of the random delay into consideration, the conservativeness in control design is reduced. A delay-dependent switching control scheme is developed by redesigning the adjacency matrix. Finally, simulation results are provided to verify the effectiveness of the proposed approach.     

一类模糊时滞系统指定衰减度的鲁棒控制

研究了一类非线性时滞系统基于模糊T-S模型的鲁棒镇定问题,所考虑的不确定时滞系统含有时变未知但有界的状态时滞,首先利用Razumikhin定理和Lyapunov定理,得出了由模糊T-S模型描述的非线性时滞系统鲁棒稳定且具有指定衰减度的判据,其次得到了具有指定衰减度的无记忆状态反馈控制律存在的充分条件及相应的控制器设计方法,该条件被进一步等价地转化为一个线性矩阵不等式的可解性问题,所设计的控制器确保了闭环系统具有指定衰减度鲁棒稳定。     

Stability analysis for discrete-time switched time-delay systems

The stability analysis problem is studied in this paper for a class of discrete-time switched time-delay systems. By using a newly constructed Lyapunov functional and the average dwell time scheme, a delay-dependent sufficient condition is derived for the considered system to be exponentially stable. The obtained results provide a solution to one of the basic problems in discrete-time switched time-delay systems, that is, to find a switching signal for which the switched time-delay system is exponentially stable. Two illustrative examples are given to demonstrate the effectiveness of the proposed results.     

一类不确定切换奇异时滞系统的时滞依赖鲁棒镇定

针对一类不确定切换奇异时滞系统,对其鲁棒镇定问题进行了研究.首先利用多李亚普诺夫泛函方法和线性矩阵不等式工具,通过引入适当的自由权矩阵,在适当的切换律下,给出了基于严格线性矩阵不等式表示的标称自治切换奇异系统正则、无脉冲且渐近稳定的时滞依赖条件;然后基于此条件,通过设计相应的状态反馈子控制器,得到了保证闭环系统对所有允许的不确定性是正则、无脉冲且渐近稳定的时滞依赖条件,同时给出了子控制器的显示表达式.数值算例表明该方法的有效性.