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.     

关于不确定对称组合系统的稳定化

研究不确定对称组合系统的二次稳定化问题,给出这类系统可二次稳定的一些充分条件 及计算反馈控制律的方法.这些条件的检验和反馈控制律的计算都由两个低阶系统关于相应 问题的求解来完成.     

对称循环组合系统的几个控制问题

研究了对称循环组合系统的输出调节问题和不确定对称循环组合的二次稳定性和二次稳定化问题。结果表明,由于对称循环组合系统结构的特殊性,这的输出调节问题可以转化为一些低价系数的输出调节问题。而不确定对称循环组合系统的二次稳定性可以通过考察若干个低价系数的二次稳定性来判断,且其稳定比化控制律也可以通过低价系数的稳定化控制律来构造。     

切换循环组合系统的基本性能分析

切换循环组合系统具有广泛的实际背景,生物学中的“超循环”是其中之一.本文研究了这种切换系统在任意切换律下的二次稳定性,循环矩阵的结构特征为解决这个问题提供了有效的方法.此外,拟循环组合系统,一种扩展的循环组合系统,也作为本文研究的对象,给出这种组合系统的简化降阶方法.最后,针对切换循环组合系统的仿真算例验证了文中的主要结果.     

凸锥型不确定线性切换系统的二次镇定

研究具有凸锥型不确定性的线性切换系统的二次鲁棒稳定化问题.这种不确定性是由若干已知常数矩阵所张成的凸锥构成的.利用凸组合技术,分别给出了连续和离散线性切换系统的鲁棒二次可稳定条件及切换律的设计方法.按照这些条件,只要判断张成凸锥的顶点矩阵的某个凸组合是否可稳即可.最后给出仿真例子.     

一类线性切换系统具有H∞性能指标的二次稳定

研究了一类线性切换系统具有H_∞扰动衰减度二次稳定问题.这类线性切换系统由两个子系统组成,并且每个子系统都不是具有H_∞扰动衰减度二次稳定的.利用单Lyapunov函数方法,得到了线性切换系统具有H_∞扰动衰减度二次稳定的充分条件,同时由凸组合系统设计出确保线性切换系统二次稳定且具有H_∞扰动衰减度的切换律.进一步,还给出了线性切换系统具有H_∞扰动衰减度二次稳定的必要条件.最后的仿真实例表明了结论的有效性.     

一类切换组合系统的分散反馈镇定

首次提出切换组合系统的概念,给出了使此系统渐近稳定的分散切换控制律的设计, 研究了带有连续控制量的组合大系统采用分散混杂状态反馈稳定化问题.     

非线性切换系统的二次镇定

研究多输入多输出非线性切换系统在任意切换律下的二次镇定问题.当非线性切换系统有一致规范型,且一致规范型的零动态在任意切换律是渐近稳定时,设计出状态反馈控制律,并构造出所有闭环子系统的共同二次Lyapunov函数,实现了这类多输入多输出非线性切换系统在任意切换策略下的二次可镇定性,所得结果也适用于线性切换系统。     

一类离散的不确定切换模糊组合系统的分散H∞控制

针对一类离散的不确定切换模糊组合系统,利用平行分布补偿算法(PDC)给出分散切换模糊控制器的设计方法,利用多Lyapunov函数方法,给出使系统稳定且H∞控制问题可解的矩阵不等式条件,并给出分散切换律设计.仿真结果表明方法的有效性.     

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.     

线性切换系统经周期切换渐近稳定性研究

研究一类含有两个子系统的线性切换系统经周期切换渐近稳定问题.首先给出了特殊周期切换,即等时切换下线性切换系统渐近稳定的充要条件;然后将所得结论进行了推广,使之适合于一般的周期切换情形,并结合自适应思想提出了实现系统周期切换的方法,使之能应用于工程实际.特别指出,一个系统可经切换达到二次稳定的充要条件是该系统可经周期切换渐近稳定.对于一类线性切换系统,采用周期切换可使切换信号的设计变得相对简单.仿真结果表明了所提出的方法简洁而有效.     

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.     

Quadratic Stabilization of Switched Uncertain Linear Systems: A Convex Combination Approach

We consider quadratic stabilization for a class of switched systems which are composed of a finite set of continuoustime linear subsystems with norm bounded uncertainties. Under the assumption that there is no single quadratically stable subsystem, if a convex combination of subsystems is quadratically stable, then we propose a state-dependent switching law, based on the convex combination of subsystems, such that the entire switched linear system is quadratically stable. When the state information is not available, we extend the discussion to designing an output-dependent switching law by constructing a robust Luenberger observer for each subsystem.      

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.     

Quadratic stabilization of switched nonlinear systems

In this paper, the problem of quadratic stabilization of multi-input multi-output switched nonlinear systems under an arbitrary switching law is investigated. When switched nonlinear systems have uniform normal form and the zero dynamics of uniform normal form is asymptotically stable under an arbitrary switching law, state feedbacks are designed and a common quadratic Lyapunov function of all the closed-loop subsystems is constructed to realize quadratic stabilizability of the class of switched nonlinear systems under an arbitrary switching law. The results of this paper are also applied to switched linear systems. Supported partially by the National Natural Science Foundation of China (Grant No. 50525721)     

Decentralised adaptive control of switched interconnected high-order nonlinear systems with unknown control direction and time-delay

This paper studies the dynamic state feedback control problem for a class of interconnected large-scale switched high-order nonlinear systems with unknown control direction and time-varying time-delay. The adaptive laws are designed to estimate the bounds of switched parameters under arbitrary switching for subsystems. The Nussbaum function is used to deal with the unknown control direction problem. By combining the backstepping and homogeneous domination technique, the decentralised adaptive control strategies are developed and the resulting closed-loop system is asymptotically stable. Finally, a simulation example is given and the results show the effectiveness of the proposed control design method.     

Quadratic stabilization of switched systems

We consider quadratic stabilization of uncertain switched systems when a switching rule is imposed on state feedback controllers of subsystems. A method is proposed to constructively design switching rules for continuous and discrete-time switched systems with norm-bounded time-varying uncertainties. The switching rules designed via this method do not rely on uncertainties, and the switched system is quadratically stabilizable via switched state feedback for all uncertainties.     

Region stability and stabilisation of switched linear systems with multiple equilibria

This paper studies stability and stabilisation issues of switched linear time-invariant systems with stable/unstable multiple equilibria. Investigation of such switched systems is motivated by a switching economic system. The well-known common Lyapunov function method is shown to be ineffecctive in analysing region stability of switched systems with multiple equilibria via a counterexample. When every subsystem has an equilibrium point and all multiple equilibria pairwise differ, this paper proposes some sufficient conditons for region stability/instability of such switched systems with respect to a region containing all multiple equilibria under arbitrary quasi-periodical switchings. These novel results imply that there may exist stable limit cycles of such switched systems. Based on the stability results, a global asymptotic region-stabilising controller, quasi-periodical switching path, and corresponding algorithm are all designed for such switched control systems. Several illustrative examples demonstrate the effectiveness and practicality of our new results.     

Stability of Delayed Switched Systems With State-Dependent Switching

This paper investigates the stability of switched systems with time-varying delay and all unstable subsystems. According to the stable convex combination, we design a state-dependent switching rule. By employing Wirtinger integral inequality and Leibniz-Newton formula, the stability results of nonlinear delayed switched systems whose nonlinear terms satisfy Lipschitz condition under the designed state-dependent switching rule are established for different assumptions on time delay. Moreover,some new stability results for linear delayed switched systems are also presented. The effectiveness of the proposed results is validated by three typical numerical examples.