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.     

线性切换系统基于范数的系统镇定条件及算法

利用向量范数理论,讨论自治线性切换系统的镇定问题,给出了系统一种基于范数的可镇定的充分条件及镇定算法,当系统在满足一定条件的前提下,可以通过适当切换使系统渐进稳定.这种方法比一般的Lyapunov函数方法更容易应用.     

一类离散时间线性切换系统的二次鲁棒镇定

针对一类具有范数有界时变不确定性的离散时间线性切换系统,研究了其二次稳定化状态反馈控制律的设计问题.利用多李亚普诺夫函数法推导了在任意切换下二次稳定化控制律存在的充分条件,该条件被进一步等价地表示成线性矩阵不等式的可解性问题.同时它的解提供了二次稳定化控制律的一个参数化表示.仿真结果验证了所提方法的有效性.     

一类具有输入时滞的切换系统的正性镇定

研究一类含有输入时滞的切换系统正性镇定问题.通过引入增广系统,将时滞作为一个切换参数,原系统的正性镇定问题转化为增广系统异步切换下的控制问题.利用对偶系统的特性,得到增广系统在平均驻留时间切换下为正且稳定的充分条件,进而设计控制器以保证闭环系统的正性和稳定性.得到的充分条件可转化为标准的线性规划问题,利用Matlab的linprog工具箱进行求解.最后,通过仿真示例验证了所得结果的有效性.     

一类线性切换系统的鲁棒状态反馈镇定

考虑一类标称系统存在共同Lyapunov函数的切换系统的鲁棒镇定问题。在不确定性不满足匹配条件下,设计出鲁棒状态反馈控制器,并在给定的切换策略下,确保闭环系统在其平衡点处渐近稳定。仿真结果表明所设计控制器是有效的。     

时变线性切换系统的指数镇定

研究满足驻留时间条件的时变线性切换系统的指数镇定问题.在一致完全可控条件下,引入带权可控性格拉姆矩阵设计出参数化的反馈控制器,利用比较原理给出状态转移矩阵的超调估计.针对驻留时间已知和未知两种情况,通过选择设计参数消除切换产生的超调影响,建立了两个指数镇定结论.最后以仿真实例验证本文结论.     

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.     

基于观测器的切换系统反馈镇定的仿真研究

研究工程系统切换优化控制问题,为提高系统的稳定性,解决观测器子系统中存在的可观测和不可观测切换问题,提出了线性切换系统的反馈镇定的设计方案.方案根据对切换系统复杂性的认识的基础上,采用构建各种类型的误差子系统函数以及各种增广子系统函数的形式,求解一个线性矩阵不等式观测器增益矩阵的问题,从而得到了可观测子系统控制律的求解方法.进行仿真的结果说明,控制方法可使观测器子系统达到稳定,证实了方法有效性.     

二阶线性切换系统指数镇定的充要条件

考虑二阶切换系统的镇定问题. 基于极坐标表示, 揭示了由锥形区域所界定的切换控制与子系统几何性质之间的自然联系. 由此, 建立了可镇定的充分必要条件; 并从代数与几何两方面刻画了镇定切换控制的特征. 进而给出了状态轨线指数收敛率的估计, 并阐释了由切换产生极限环与滑模运动的机理. 数值例子详细说明了结论的有效性.     

离散多平衡点正切换系统有限区间稳定与镇定

在切换事件中,外界环境的干扰或者事物自身的发展变化会导致多平衡点现象.此时,多平衡点切换系统模型比传统的切换系统模型更适合描述此类事件.因此本文研究离散多平衡点正切换线性系统在有限时间区间上的稳定性与镇定性.第1,给出离散多平衡点线性切换系统为正的充要条件.第2,提出离散多平衡点正切换线性系统在有限时间区间上稳定的概念.第3,通过构造合适的Lyapunov函数以及合理分配系统的驻留时间与切换次数,针对部分子系统不稳定的离散多平衡点正切换线性系统,建立所考虑的自治系统有限时间稳定的充分条件.第4,给出非自治多平衡点正切换线性系统的控制器设计.最后,仿真例子验证理论结果的正确性.     

Stabilization of discrete-time positive switched linear systems: A nonzero elements chain method

This article studies the stability problem of discrete-time positive switched linear systems by introducing a nonzero elements chain method. Compared to existing works, the highlight of this article is reflected in the inclusiveness of the subsystem, that is, each subsystem is allowed to be stable, marginally stable or even unstable. Some sufficient conditions depending on the characteristics of system matrices and the time-dependent switching signals are established, so as to guarantee the exponential stability of positive switched linear systems. In addition, the main result is extended to the case of time-varying delay. At last, the superiority of the obtained results is well verified by numerical examples.     

Two slow stabilizing switching laws for discrete time positive switched systems

On the basis of a linear copositive Lyapunov function (LF) and a diagonal quadratic LF, respectively, two slow stabilizing switching laws are proposed for discrete time positive switched systems composed of subsystems. Under these two stabilizing switching laws, the LFs are allowed to increase in state‐driven intervals while the stability of positive switched systems is maintained. In addition, it is shown that positive switched systems under these two slow switching laws are robust against certain classes of perturbations. Furthermore, when the states of the systems are not available, observer‐based stabilizing switching laws for positive switched systems are also proposed. Some numerical examples are finally given to illustrate the effectiveness of the proposed stabilizing switching laws. Copyright © 2013 John Wiley & Sons, Ltd.     

Positive stabilization for switched linear systems under asynchronous switching

This paper is concerned with the positive stabilization for a class of switched systems under asynchronous switching signals. Because it inevitably takes some time to identify the active subsystem in the real systems and activate the corresponding controller, the switching of controllers lags behind that of subsystems, which arises the problem of the asynchronous switching. By analyzing the solution of dynamic systems, the mode‐dependent controllers are designed to guarantee the positivity and exponential stability for the resultant closed‐loop switched linear systems under asynchronous switching signals in continuous‐time and discrete‐time cases, respectively. Sufficient conditions for the existence of admissible state‐feedback controllers are developed, and the corresponding switching signals are designed. Furthermore, a synchronous switching phenomenon is discussed as a special case. Finally, numerical examples are given to illustrate the effectiveness of the results. Copyright © 2015 John Wiley & Sons, Ltd.     

离散时间切换线性系统的最小状态超调设计

本文探讨离散时间切换线性系统的最小状态超调设计问题. 对有限时长情形, 给出基于穷尽搜索的构造性 算法, 并采用降价法提高计算效率. 对无限时长情形, 给出基于分段总汇的次优设计方案     

Model order-reduction for discrete-time switched linear systems

This article describes the problem of model order-reduction for a class of hybrid discrete-time switched linear systems composed of linear discrete-time invariant subsystems with a switching rule. This article investigates two novel approaches to model order-reduction. The first approach consists in evaluating the error approximation performance; the problems are solved using the robust stability results of the switched systems. The second approach presents the reachability and observability Gramians of the switched systems, which allows a balanced truncation model reduction procedure. A numerical example shows the effectiveness of the proposed approaches.     

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.     

Dissipativity and dissipative control for positive switched systems: A multiple linear copositive storage function method

In this article, the problems of dissipativity analysis and dissipative control are investigated for positive switched linear systems in both continuous and discrete‐time domains. We aim at solving the problems via employing a multiple linear copositive storage function scheme. The solvability of the problems for individual subsystem is only on their active regions. Switching laws and a set of feedback controllers are jointly devised such that the associated closed‐loop switched systems are not only positive but also dissipative, which is from the exogenous input to the output. Asymptotic stability is derived if all subsystems are zero‐state detectable. Moreover, sufficient conditions guaranteeing dissipativity with positivity constraint are presented, which can be easily examined on the grounds of linear programming approach. Finally, an example is offered, illustrating that the proposed control strategy is successful.     

A common linear copositive Lyapunov function for switched positive linear systems with commutable subsystems

This article is concerned with the existence problem of a common linear copositive Lyapunov function (CLCLF) for switched positive linear systems with stable and pairwise commutable subsystems. Three families of such systems composed of only continuous-time subsystems, only discrete-time subsystems and mixed continuous- and discrete-time subsystems are considered, respectively. It is demonstrated that a CLCLF can always be constructed for the underlying system whenever its subsystems are continuous-time, discrete-time or the mixed type. The case when the number of subsystems is two is first considered, then the obtained result is extended to the general case. Three numerical examples are given to verify the validity of the developed results.     

Asynchronous switching output feedback control of discrete-time switched linear systems

In this paper, the problem of dynamic output-feedback control synthesis is addressed for discrete-time switched linear systems under asynchronous switching. The proposed hybrid controller consists of a standard dynamic output-feedback switching control law and an impulsive reset law induced by controller state jumps. Using the average dwell time technique incorporating with multiple quadratic Lyapunov functions, the switching control synthesis conditions for asymptotic stability with guaranteed weighted ?₂-gain performance are derived as a set of linear matrix inequalities (LMIs). The proposed hybrid synthesis scheme advances existing design methods for output-feedback asynchronous switching control of switched linear systems in two important aspects: LMI formulation of the synthesis problem; and arbitrary order of the controller state. A numerical example is used to illustrate the effectiveness and advantages of the proposed design technique.