带有时滞摄动的线性切换系统的稳定性

研究一类带有时滞摄动的线性切换系统的稳定性，分别利用单李亚普诺夫函数方法和多李亚普诺夫函数方法给出了使切换系统渐近稳定的条件和切换律的设计方法。仿真结果验证了所提出设计方法的有效性。     

切换线性超循环系统的稳定性分析

超循环---生物学中重要模型, 具有广泛的实际背景. 本文将超循环系统扩展为切换超循环系统. 循环矩阵的循环结构为研究切换超循环系统的稳定性提供了有效的方法, 给出切换线性时变超循环系统在任意切换律下渐近稳定的充要条件和切换线性定常超循环系统可切换镇定的充分条件.     

具有异维数子系统的切换系统稳定性分析

研究一类线性切换系统的稳定性问题.该类切换系统包含2个不同维数的线性子系统.首先根据原系统的结构,构造出它的比较切换系统;然后设计出比较系统的切换率,在保证每个线性子系统的被激活时间均大于某一数值τ(＞0)的情况下,构造出2个子系统的Lyapunov函数;随后利用线性矩阵不等式(LMI)的方法给出每个子系统渐近稳定的条件.进一步利用Lyapunov稳定性理论的方法,保证整个比较系统的渐进稳定性,进而给出了原切换系统达到渐近稳定的一个充分条件.最后,一个数值例子说明文中方法的有效性.     

离散时滞切换系统稳定性分析

对于一类子系统为离散时滞系统的切换系统,研究渐近稳定性条件和切换信号的选取方法．根据李亚普诺夫稳定性理论，推出以线性矩阵不等式表示的在任意切换信号作用下系统渐近稳定的两个充分性条件，在此基础上进一步给出了系统渐近稳定的凸组合条件和切换信号的选取方法．仿真实例验证了所设计的切换方案的有效性．     

基于遗传算法的切换控制器设计与优化

利用遗传算法研究了一类切换规则只由状态决定的切换系统的控制器优化设计问题.首先由线性矩阵不等式(LMI)来设计切换控制器,然后应用遗传算法来对切换规则进行优化.优化后的切换规则不仅可保证闭环系统渐近稳定,而且具有良好的动态性能.将本文提出的方法应用在小车倒立摆控制系统上,仿真结果表明了本文设计方法的有效性.     

一类带有时滞的不确定广义系统的切换渐近稳定性

研究了一类带有时滞的切换不确定广义系统的鲁棒渐近稳定问题. 利用Lyapunov稳定性定理和线性矩阵不等式(Linear matrix inequality, LMI)工具, 采用多Lyapunov函数技术, 在设定的切换律下, 得到切换不确定广义时滞系统鲁棒渐近稳定的时滞相关充分条件. 进一步, 建立了一个具有线性矩阵不等式约束的凸优化问题, 利用Matlab软件中的LMI工具箱求解, 得到保证切换广义系统鲁棒渐近稳定的最大可允许时滞上界. 最后示例表明了该方法的有效性.     

等时切换下线性切换系统的稳定性及鲁棒稳定性研究-LMI方法

研究等时切换下线性切换系统的稳定性及鲁棒稳定性问题。文中首先提出等时切换的概念。然后利用LMI方法推导出等时切换下线性系统稳定及鲁棒稳定的充要条件，使用这两个充要条件可以将文中研究的复杂问题转化为相应的易处理的线性系统的问题，再利用线性系统已有的结论使问题得到解决。使用上述结果，本文为系统设计了鲁棒控制器。文中还给出实现线性切换系统等时切换的具体方法，这使等时切换方法可以真正应用于工程实践。大量仿真证实文中所提出的方法简洁、有效。     

连续线性切换系统的镇定慢切换设计

针对含有两个不稳定子系统的线性切换系统,设计一种包含时间驱动和状态驱动两个环节的切换法则,使线性切换系统稳定.在该切换法则下,系统的类Lyapunov函数在两个环节都不需要严格单调递减,使得系统在每个子系统有更长的驻留时间,从而有效降低系统的切换频率.在适当的假设条件下,带时变扰动的线性切换系统在该切换信号下具有良好的鲁棒稳定性.基于此,当系统可观测时,进一步设计了基于观测器的混合切换法则,实现了系统的鲁棒稳定.     

切换对称组合系统的稳定性

首次提出了切换对称组合系统的概念, 研究了此类系统在任意切换下渐近稳定的条件, 同时分别利用多李雅普诺夫函数方法和单李雅普诺夫函数方法, 给出使切换对称组合系统渐近稳定的切换律, 利用切换对称组合系统的结构特点, 使其切换律的设计条件得到简化.     

一类离散切换模糊系统的稳定性

针对离散模糊系统,提出一类离散切换模糊系统的稳定性问题.使用切换技术及单Lyapunov函数、多Lyapunov函数方法构造出连续状态反馈控制器,使得相应的闭环系统渐近稳定,同时设计可以实现系统全局渐近稳定的切换律.模型中的每个切换系统的子系统是离散模糊系统,取常用的平行分布补偿PDC控制器,主要条件以凸组合和矩阵不等式的形式给出,具有较强的可解性.计算机仿真结果表明设计方法的可行性与有效性.     

Critical dwell time of switched linear systems

In this paper, we consider the relation between the switching dwell time and the stabilization of switched linear control systems. First of all, a concept of critical dwell time is given for switched linear systems without control inputs, and the critical dwell time is taken as an arbitrary given positive constant for a switched linear control systems with controllable switching models. Secondly, when a switched linear system has many stabilizable switching models, the problem of stabilization of the overall system is considered. An on-line feedback control is designed such that the overall system is asymptotically stabilizable under switching laws which depend only on those of uncontrollable subsystems of the switching models. Finally, when a switched system is partially controllable （While some switching models are probably unstabilizable）, an on-line feedback control and a cyclic switching strategy are designed such that the overall system is asymptotically stabilizable if all switching models of this uncontrollable subsystems are asymptotically stable. In addition, algorithms for designing switching laws and controls are presented.     

Critical dwell time of switched linear systems

In this paper, we consider the relation between the switching dwell time and the stabilization of switched linear control systems. First of all, a concept of critical dwell time is given for switched linear systems without control inputs, and the critical dwell time is taken as an arbitrary given positive constant for a switched linear control systems with controllable switching models. Secondly, when a switched linear system has many stabilizable switching models, the problem of stabilization of the overall system is considered. An on-line feedback control is designed such that the overall system is asymptotically stabilizable under switching laws which depend only on those of uncontrollable subsystems of the switching models. Finally, when a switched system is partially controllable (While some switching models are probably unstabilizable), an on-line feedback control and a cyclic switching strategy are designed such that the overall system is asymptotically stabilizable if all switching models of this uncontrollable subsystems are asymptotically stable. In addition, algorithms for designing switching laws and controls are presented.     

Design of two-layer switching rule for stabilization of switched linear systems with mismatched switching

A two-layer switching architecture and a two-layer switching rule for stabilization of switched linear control systems are proposed, under which the mismatched switching between switched systems and their candidate hybrid controllers can be allowed. In the low layer, a state-dependent switching rule with a dwell time constraint to exponentially stabilize switched linear systems is given; in the high layer, supervisory conditions on the mismatched switching frequency and the mismatched switching ratio are presented, under which the closed-loop switched system is still exponentially stable in case of the candidate controller switches delay with respect to the subsystems. Different from the traditional switching rule, the two-layer switching architecture and switching rule have robustness, which in some extend permit mismatched switching between switched subsystems and their candidate controllers.     

Stability analysis and control synthesis of switched impulsive systems

In this paper, we investigate the stability analysis problem of switched impulsive nonlinear systems and several stabilization problems of switched discrete‐time linear systems are studied. First, sufficient conditions ensuring globally uniformly asymptotically stability of switched nonlinear impulsive system under arbitrary and DDT (dynamical dwell time which defines the length of the time interval between two successive switchings) switching are derived, respectively. In the DDT switching case, we first consider the switched system composed by stable subsystems, then we extend the results to the case where not all subsystems are stable. The stabilizations of switched discrete‐time linear system under arbitrary switching, DDT switching and asynchronous switching are investigated respectively. Based on the stability analysis results, the control synthesis consists of controller design for each subsystem and state impulsive jumping generators design at switching instant. With the aid of the state impulsive jumping generators at switching instant, the ‘energy’ produced by switching can be minimized, which leads to less conservative results. Several numerical examples are given to illustrate the proposed results within this paper. Copyright © 2011 John Wiley & Sons, Ltd.     

Growth rate of switched homogeneous systems

We consider discrete-time homogeneous systems under arbitrary switching and study their growth rate, the analogue of joint spectral radius for switched linear systems. We show that a system is asymptotically stable if and only if its growth rate is less than unity. We also provide an approximation algorithm to compute growth rate with arbitrary accuracy.     

一类不受控离散事件驱动不确定线性切换系统优化控制

考虑一类不受控离散事件驱动不确定约束线性切换系统, 提出具有任意切换特性的约束优化控制策略. 引入有限时域性能函数, 定义约束最优控制问题. 为降低控制器的在线计算量, 通过参数化方法压缩最优控制问题决策变量的维数. 应用公共Lyapunov 函数和控制Lyapunov 函数理论建立的闭环切换系统, 具有对不确定扰动和不受控切换信号的渐近稳定性和逆最优性. 最后通过算例仿真验证了结果的有效性.

     

Robust stability analysis of uncertain switched linear systems with unstable subsystems

The problem of robust stability for switched linear systems with all the subsystems being unstable is investigated. Unlike the most existing results in which each switching mode in the system is asymptotically stable, the subsystems may be unstable in this paper. A necessary condition of stability for switched linear systems is first obtained with certain hypothesis. Then, under two assumptions, sufficient conditions of exponential stability for both deterministic and uncertain switched linear systems are presented by using the invariant subspace theory and average dwell time method. Moreover, we further develop multiple Lyapunov functions and propose a method for constructing multiple Lyapunov functions for the considered switched linear systems with certain switching law. Several examples are included to show the effectiveness of the theoretical findings.     

Stabilisability of nonlinear systems by means of time-dependent switching rules

Given a family of linear systems which admit an asymptotically stable convex combination, the existence of stabilising time-dependent switching rules can be proved by using the Baker–Campbell–Hausdorff formula for exponentials. The control laws obtained in this way are periodic, fast switching and independent of the initial state. We prove that under a similar assumption, the approach can be extended to provide stabilising time-dependent switching rules for the families of nonlinear vector fields, as well. However, the resulting control law, in general, is not periodic, not fast switching and it may depend on the initial state.     

An extension of LaSalle’s Invariance Principle for a class of switched linear systems

In this paper LaSalle’s Invariance Principle for switched linear systems is studied. Unlike most existing results in which each switching mode in the system needs to be asymptotically stable, in this paper the switching modes are allowed to be only Lyapunov stable. Under certain ergodicity assumptions, an extension of LaSalle’s Invariance Principle for global asymptotic stability of switched linear systems is proposed provided that the kernels of derivatives of a common quadratic Lyapunov function with respect to the switching modes are disjoint (except the origin).