一类时滞切换系统的输入-状态稳定性分析

利用多Lyapunov函数方法、驻留时间法和Gronwall-Bellman不等式研究了一类时滞切换系统的输入-状态稳定性分析问题．从系统输入-状态稳定定义出发,给出了使得一类时滞切换系统输入-状态稳定的充分条件．与已有的方法相比,无需同时满足构造输入-状态稳定控制Lyapunov函数和所有子系统都是输入-状态稳定的条件,为控制器的设计提供了便利．最后,通过算例仿真验证了所提出方法的可行性．     

一类切换系统的输入-状态稳定性分析与优化控制

利用驻留时间法和 Gronwall-Bellman不等式研究了一类切换系统的输入一状态稳定性分析与优化控制问题.在保证切换系统输入-状态稳定的前提下,将切换时刻和切换次数约束条件转化为线性约束,提出了一种新的切换系统优化问题目标函数的形式.与已有的方法相比,该方法无需引入新的状态变量,无需同时满足构造输入-状态稳定控制李亚普诺夫函数和所有子系统都是输入-状态稳定的条件,为控制器的优化设计提供了便利.最后,通过算例仿真证实了文中所提方法的可行性.     

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.     

一类非线性切换系统的观测器设计

研究了一类切换规则为时间依赖型的非线性切换系统的观测器设计问题．分别在切换序列已知与平均驻留时间已知的情况下利用线性矩阵不等式（LMI）给出了非线性项满足Lipschitz条件的切换系统的观测器增益求解方法,并给出了观测器设计步骤．最后给出仿真算例说明了本文方法的有效性．     

切换系统输入对状态稳定性的充分条件

研究了切换系统输入对状态的稳定性.在所有子系统都是输入对状态稳定的条件下,利用各子系统的KY函数和K函数构造出切换系统所需的KY函数和X函数,从而给出了切换系统输入对状态稳定的充分条件.对于一类常见的切换系统,计算出保证输入对状态稳定性的切换停留时间的下界,所有结果都是构造性的.     

具有脉冲作用的切换线性广义系统的稳定性

本文引入一类新的系统模型—具有脉冲作用的切换线性广义系统. 应用驻留时间(Dwell time)方法和平均驻留时间(Average dwell time)方法研究其稳定性问题, 并给出系统指数稳定性的充分条件. 证明了当平均驻留时间足够大且重设律是允许的, 那么系统是指数稳定的. 利用广义系统的受限等价性质, 具体给出允许的重设律的设计方法. 数值例子说明本文方法的有效性.     

不确定切换时滞非线性系统状态切换的指数稳定性

利用状态依赖控制策略对切换信号进行设计,使得一类参数不确定时滞非线性切换系统指数稳定且具有一定的??∞抗干扰性能。利用Lyapunov-Krasovskii (LK)函数方法,以线性矩阵不等式组的方式,给出了稳定切换律存在的充分条件,并且该系统是指数稳定的。通过引入自由矩阵并结合积分不等式技巧,得到了保守性较低的稳定性条件。仿真算例表明了所提出方法的有效性和较低的保守性。     

带有不稳定子系统的切换非线性系统的积分输入状态稳定

本文针对带有不稳定子系统的切换非线性系统研究了系统的积分输入状态稳定性问题. 应用导数不定的 类Lyapunov函数得出切换非线性系统的积分输入状态稳定. 导数不定的类Lyapunov函数方法比传统的导数正定 的Lyapunov函数的方法更具有一般性. 文中包含两种情况: 当所有子系统为积分输入状态稳定时, 切换非线性系统 是积分输入状态稳定的; 当部分子系统为非积分输入状态稳定时, 本文证明了切换非线性系统的积分输入状态稳 定. 最后应用一个仿真例子描述了所提结果的有效性.     

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.     

Input-to-state stability of switched nonlinear systems

The input-to-state stability （ISS） problem is studied for switched systems with infinite subsystems. By using multiple Lyapunov function method, a sufficient ISS condition is given based on a quantitative relation of the control and the values of the Lyapunov functions of the subsystems before and after the switching instants. In terms of the average dwell-time of the switching laws, some sufficient ISS conditions are obtained for switched nonlinear systems and switched linear systems, respectively.     

Global exponential stability of 2D switched positive nonlinear systems described by the Roesser model

In this paper, we aim to investigate the stability of 2D switched positive nonlinear systems with time‐varying delays in the Roesser model, which includes 2D switched positive linear systems as a special case. By using the average dwell time approach, we give a sufficient condition for the exponential stability of 2D switched positive nonlinear systems. The difficulty caused by the delays is overcome by introducing a model transform and the method used in this paper is different from conventional Lyapunov‐Krasovskii functional method. An explicit exponential bound on the decay rate is presented. We also extend the result to the general 2D switched linear systems, not necessarily positive. Finally, an illustrative example is given to demonstrate the effectiveness of the obtained result.     

Input‐to‐state stability of switched nonlinear systems with delay in the active mode detection

A switched nonlinear system subject to disturbances is considered in this paper. The switching signal admits an average dwell time and a state feedback control depending on the system operating modes, detected with a maximum time delay, is applied to the system. In this framework, the input‐to‐state stability problem of the closed‐loop system is addressed. Based on some established existence conditions of mode‐dependent Lyapunov‐like functions, the values of the maximum time delay and the average dwell time that allow to achieve the input‐to‐state stability of the closed‐loop system are determined. In order to obtain more tractable results, the existence conditions of the mode‐dependent Lyapunov‐like functions are given in terms of sum‐of‐squares programming in the case of polynomial nonlinearities. In the linear case, they are expressed in terms of linear matrix inequalities and a procedure for the synthesis of the mode‐dependent controller is provided in this situation. The established theoretical results are illustrated through a control problem of a building ventilation system and a switched control problem of a vehicle suspension system.     

Average dwell time based stability analysis for nonautonomous continuous‐time switched systems

Inspired by the idea of multiple Lyapunov functions and the average dwell time, we address the stability analysis of nonautonomous continuous‐time switched systems. First, we investigate nonautonomous continuous‐time switched nonlinear systems and successively propose sufficient conditions for their (uniform) stability, global (uniform) asymptotic stability, and global (uniform) exponential stability, in which an indefinite scalar function is utilized to release the nonincreasing requirements of the classical multiple Lyapunov functions. Afterwards, by using multiple Lyapunov functions of quadratic form, we obtain the corresponding sufficient conditions for (uniform) stability, global (uniform) asymptotic stability, and global exponential stability of nonautonomous switched linear systems. Finally, we consider the computation issue of our current results for a special class of nonautonomous switched systems (ie, rational nonautonomous switched systems), associated with two illustrative examples.     

任意相对阶下非线性切换系统的事件触发漏斗控制

针对一类具有任意相对阶且带有部分非输入到状态稳定逆动态的非线性切换系统, 提出一种动态事件触 发漏斗跟踪控制方案. 首先, 引入一个虚拟输出将任意相对阶的非线性切换系统转换为相对阶为一的非线性切换系 统. 其次, 设计各子系统的事件触发漏斗控制器和切换的动态事件触发机制, 解决候选事件触发漏斗控制器和子系 统之间的异步切换问题, 所提方案消除已有文献中为所有子系统设计共同控制器带来的保守性. 在一类具有平均驻 留时间切换信号的作用下, 保证切换闭环系统的所有信号都是有界的, 且跟踪误差一直在预设的漏斗内演化, 并排 除采样中的奇诺现象. 最后, 一个仿真例子验证方案的实用性和有效性.     

Output tracking control of cascade switched nonlinear systems

The output tracking problem for cascade switched nonlinear systems is studied based on the average dwell time method in this paper. Sufficient conditions for this problem to be solvable are derived, where the zero dynamics is unstabilisable under an arbitrary switching. When the switching signal satisfies an average dwell time scheme, H_∞ output tracking is achieved by virtue of a designed switched integral controller. A numerical example is illustrated to show the effectiveness of the main result.     

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.     

Input-to-state stability for discrete-time time-varying impulsive switched delayed systems with asynchronous phenomena

This paper studies the input-to-state stability (ISS) for a class of discrete-time time-varying impulsive switched delayed systems, in which the asynchronous phenomena are considered. Asynchronous phenomena here include two implications: asynchronous impulses and switches and asynchronous switching. The former means that the events, that is, impulses and switches, are not necessary to occur simultaneously, while the latter indicates that the actual switching modes and related controllers or specified modes do not coincide. Applying the mode-dependent concept to impulses and switches, both the improved Krasovskii-type and Razumikhin-type ISS criteria are provided. The time differences of Lyapunov functionals or functions here are sign-changing and time-varying, releasing from the traditional assumption that always requires negative definiteness. Meanwhile, in this paper, ISS or non-ISS subsystems and stabilizing or destabilizing impulses are taken into account. Finally, three numerical examples are given to illustrate the effectiveness of the proposed results.