时变时滞连续切换奇异系统的一致有限时间稳定分析

讨论一类含有时变时滞的连续时间切换奇异系统的一致有限时间稳定、有限时间有界和状态反馈镇定问题. 在给定任意的切换规则下, 运用多Lyapunov 函数和平均驻留时间方法设计使得闭环系统一致有限时间稳定和有限时间有界的状态反馈控制器, 同时给出基于线性矩阵不等式表示的控制器存在的充分条件. 最后通过数值算例表明了所提出方法的合理性和有效性.

     

基于模型依赖平均驻留时间的线性切换系统有限时间??∞ 控制

针对一类具有有界干扰的线性切换系统研究其有限时间鲁棒控制问题。基于模型依赖平均驻留时间,提出了系统有限时间有界且具有H∞性能指标的充分条件,与传统方法中系统具有单一平均驻留时间不同,各切换子系统具有各自的平均驻留时间,因而降低了设计的保守性。进一步,将切换系统的有限时间状态反馈控制器设计转化为具有线性矩阵不等式约束的优化问题。数值算例和仿真对比表明,所提出的方法增加了切换律设计的自由度。     

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.     

基于有限时间的一类时滞非线性切换系统滑模控制

研究一类时滞非线性切换系统的有限时间滑模控制问题.针对所研究的系统模型,构造每个子系统对应的积分滑模面,基于滑模控制理论,设计带有状态时滞的滑模控制器使得每个子系统能在有限时间内到达相应的滑模面上,并对系统中存在的非线性项采用Lipschitz条件进行处理.根据多李亚普诺夫函数、平均驻留时间方法以及分割策略引理,给出滑模趋近段和滑模动态有限时间有界的充分条件,并通过对线性矩阵不等式的求解得到控制器增益.最后,通过一个数值仿真例子验证该设计方法的有效性.     

离散线性切换系统的一致有限时间稳定分析和反馈控制及其在网络控制系统中的应用

研究了一类离散线性切换系统的一致有限时间稳定性分析和反馈镇定．基于线性矩阵不等式技术,给出了在任意切换信号作用下,离散线性切换系统有限时间稳定和有限时间有界的充分条件,并给出了离散线性切换控制系统一致有限时间状态反馈控制器的设计方法．将上述分析结果应用于一类丢包有界的网络控制系统,得到了保证其有限时间稳定的反馈控制器．最后,通过两个数值仿真例子验证了所提方法的有效性．     

T-S模糊系统的有限时间控制

面向具有强非线性的复杂工业过程,利用T-S模糊模型逼近原非线性系统,把T-S模糊模型逼近非线性系统存在的误差描述成有界时变的扰动,进而提出带扰动的T-S模糊系统的有限时间控制方法.首先,给出线性系统有限时间有界性的一个充分条件,与现有结果相比,该条件具有较小的保守性,并可以处理扰动是时变的情况;然后,提出T-S模糊系统有限时间镇定控制器的设计方法;最后,给出基于线性矩阵不等式(LMI)的控制器设计算法,并通过数值算倒演示所给方法的有效性.     

离散随机Markov跳跃系统有限时间有界控制

研究一类带乘性噪声的离散时间随机Markov跳跃系统的有限时间控制问题.首先,定义系统的有限时间稳定和有限时间有界,通过逐次迭代和条件期望给出系统有限时间稳定的充分必要条件;其次,针对含干扰的系统,利用Lyapunov方法和线性矩阵不等式技术得到系统有限时间有界的充分条件并设计状态反馈镇定控制器;然后,进一步考虑转移概率信息不完全下的有限时间有界问题;最后,通过数值例子验证了所提出方法的有效性.     

基于观测器的网络切换模糊时滞系统鲁棒控制

针对带有随机时变时滞的非线性网络切换系统稳定控制问题进行研究,在系统状态不可测且存在不确定性的情况下,采用T-S模型将非线性网络切换系统建模为网络切换模糊系统。然后,采用平均驻留时间法（ADT）,设计出基于观测器的控制器及系统切换律,并给出网络切换模糊系统指数稳定的平均驻留时间条件。结合李雅普诺夫（LKF）方法给出时滞相关的网络切换模糊系统指数稳定的矩阵不等式条件。最后通过MATLAB数值仿真验证了该设计方法的有效性和优越性。     

不确定奇异系统的有限时间H_∞控制

针对一类在有限时间下的线性奇异系统,同时考虑参数不确定性和有限外部扰动影响,研究了系统基于状态反馈控制器的鲁棒H∞控制问题。首先通过构造合适的Lypunov函数,利用线性矩阵不等式方法给出了线性广义系统有限时间有界且H∞范数有界的充分条件,在此基础上讨论线性广义系统的H∞状态反馈控制,给出了控制器存在的充分条件,同时给出了控制器的具体设计方法,控制器可由线性矩阵不等式解得。最后的数值算例说明了所提出方法的可行性和有效性。     

切换非线性正系统的有限时间稳定性

研究模型依赖平均驻留时间(MDADT)切换信号下一类齐次度为1的切换非线性正系统的有限时间稳定问题.首先,通过构造恰当的切换最大分离Lyapunov函数,借助于Dini导数,基于MDADT切换信号,给出切换非线性正系统有限时间稳定的充分条件.与已有的指数稳定性结果相比,进一步说明有限时间稳定与指数稳定的区别.其次,将所得结论应用于切换线性正系统,得到切换线性正系统在MDADT或平均驻留时间(ADT)切换信号下有限时间稳定的充分条件.最后,通过仿真算例验证所得结论的有效性.     

Control discrete-time switched singular systems with state delays under asynchronous switching

This article is concerned with the problem of state feedback control for a class of discrete-time switched singular systems with time-varying state delays under asynchronous switching. The asynchronous switching considered here means that the switching instants of the candidate controllers lag behind those of the system modes. The concept of mismatched control rate is introduced. By using the multiple Lyapunov function approach and the average dwell time technique, a sufficient condition for the existence a stabilising switching law is first derived to guarantee the regularity, causality and exponential stability of the closed-loop system in the presence of asynchronous switching. The stabilising switching law is characterised by a upper bound on the mismatched control rate and a lower bound on the average dwell time. Then, the corresponding solvability condition for a set of mode-dependent state feedback controllers is established by using the linear matrix inequality (LMI) technique. Finally, a numerical example is provided to illustrate the effectiveness of the proposed method.     

Finite‐time stability of fractional order impulsive switched systems

This paper considers the finite‐time stability of fractional order impulsive switched systems. First, by using the fractional order Lyapunov function, Mittag–Leffler function, and Gronwall–Bellman lemma, two sufficient conditions are given to verify the finite‐time stability of fractional order nonlinear systems. Then, the concept of finite‐time stability is extended to fractional order impulsive switched systems. A sufficient condition is given to verify the finite‐time stability of fractional order impulsive switched systems by combining the method of average dwell time with fractional order Lyapunov function. Finally, two numerical examples are provided to illustrate the theoretical results. Copyright © 2014 John Wiley & Sons, Ltd.     

Finite‐time stability of switched positive linear systems

This brief paper addresses the finite‐time stability problem of switched positive linear systems. First, the concept of finite‐time stability is extended to positive linear systems and switched positive linear systems. Then, by using the state transition matrix of the system and copositive Lyapunov function, we present a necessary and sufficient condition and a sufficient condition for finite‐time stability of positive linear systems. Furthermore, two sufficient conditions for finite‐time stability of switched positive linear systems are given by using the common copositive Lyapunov function and multiple copositive Lyapunov functions, a class of switching signals with average dwell time is designed to stabilize the system, and a computational method for vector functions used to construct the Lyapunov function of systems is proposed. Finally, a concrete application is provided to demonstrate the effectiveness of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.     

线性切换系统的采样数据输出调节问题

本文基于采样控制,解决了线性切换系统的输出调节问题.首先考虑了外部输入信号是常数的情况,给出了采样周期与平均驻留时间的关系.通过构造一类Lyapunov-Krasovskii泛函,使得闭环系统内部稳定且调节输出趋于零.其次考虑了外部输入信号是导数有界且时变的情况,给出了采样数据状态反馈控制器,并依据采样周期和平均驻留时间关系给出的切换条件得到了切换系统实用输出调节问题可解的充分条件.最后通过两个数值例子验证了方法的有效性.     

基于模型依赖驻留时间的异步切换控制

研究在模型依赖平均驻留时间切换策略下切换线性系统的异步切换控制问题,同时考虑模型依赖的控制器滞后时间的约束问题.在实际情况下,信号传输和系统检测等原因会导致控制器的切换滞后于子系统.基于这类情况,首先将子系统运行的区间划分为子系统与控制器相匹配的区间和非匹配的区间,根据模型依赖的驻留时间策略设计出各子系统的控制器;然后,结合模型依赖的控制器滞后时间、系统参数和Lyapunov稳定条件推导出合适的驻留时间设计参数,且使得异步切换系统全局一致指数稳定;最后通过数值仿真验证了所提出方法的有效性.     

Finite‐time boundedness and L2‐gain analysis for switched positive linear systems with multiple time delays

In this paper, we study the finite‐time boundedness, stabilization, and L₂‐gain for switched positive linear systems (SPLS) with multiple time delays. Using multiple linear copositive Lyapunov functions, sufficient conditions in terms of linear matrix inequalities are obtained for the problems of finite‐time boundedness and stabilization and the design of state feedback controllers for SPLS. Under asynchronous switching, L₂‐gain analysis is developed for SPLS under the constraint of average dwell time. Numerical examples are given to illustrate our theoretical results. Copyright © 2017 John Wiley & Sons, Ltd.     

Decentralised H∞ finite-time control equation of large-scale switched systems using robust performance minimisation

Many actual engineering applications can be modelled as large-scale switched system, while switching behaviours often occur in some short finite time intervals; thus, it is significant to ensure the finite-time boundedness of large-scale switched system in practical terms. In this paper, the problems of finite-time stability analysis and stabilisation for large-scale switched system are addressed. First, considering different switching signals for subsystems, the concepts of decentralised finite-time boundedness (DFTB) and decentralised finite-time H_∞ controllers are introduced, which focus on the dynamical transient behaviour of large-scale switched system during finite intervals. Under these concepts, several sufficient conditions are given to ensure a class of large-scale systems decentralised finite-time stable based on the decentralised average dwell times, and then the results are extended to H_∞ finite-time boundedness of large-scale switched system. Finally, based on the results on DFTB, optimal decentralised H_∞ controllers and average dwell times are designed under the minimum value of H_∞ performance. Numerical examples are given to illustrate the effectiveness of the proposed approaches in this paper.