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．     

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。     

一类线性不确定时滞混杂系统的稳定性

研究了一类具有不确定的线性参数及时滞的混杂系统，利用线性矩阵不等式策略和Riccati方法，给出了系统鲁棒稳定性和可稳定性的充分条件，并运用混杂状态反馈控制策略设计了控制器切换方案．最后的仿真实例表明了控制策略的有效性．     

一类离散时间切换系统鲁棒控制器设计

考虑一类非线性离散时间切换系统的鲁棒二次镇定和渐近镇定问题．利用公共李亚普诺夫函数方法和多李亚普诺夫函数方法，分别设计了切换系统鲁棒状态反馈控制器和输出反馈控制器，保证了切换系统的二次稳定性和渐近稳定性．仿真结果验证了所提出算法的有效性．     

一类切换线性系统的稳定性判别方法

研究了子系统中系统矩阵为对角标准型或者Jordan标准型的切换线性系统的稳定性．用状态方程的解来分析系统能量函数（状态向量的2范数）的单调性,得到系统在任意切换序列下渐近稳定的充分条件．另外,根据这些条件可以比较容易地设计出渐近稳定的切换序列．最后通过一个数值例子来说明所得到结论的效果．     

稳定性切换点法在时滞系统的鲁棒稳定性中的应用

讨论了一类参数与时滞相关的时滞系统的鲁棒稳定性.在"稳定性切换几何判据法"的基础上提出了"稳定性切换点法",使用该方法可得到相应方程零解稳定的参数变化区域.针对向日葵方程这一实际例子,利用文中所提出的方法并结合Maple软件作图可以容易地得到稳定性区域和不稳定性区域以及两区域的分界线、Hopf分岔点等;进一步通过对时滞...     

一种新的类Lorenz系统的混沌行为与形成机制

提出一种新的类Lorenz系统,它具有三维二次型的自治常微分方程组形式．理论分析中,应用Lyapunov判定方法研究了系统平衡点的稳定性．在此基础之上,数值仿真表明,文中所考查的动力学系统具有极其丰富的动力学现象．包括混沌和多种形式的周期运动形式．文中还分析了两个重要参数对系统稳定性的影响,并通过构建一个受控系统分析了系统混沌吸引子的形成机制．     

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。     

具有松弛条件的一类切换模糊系统的稳定性分析

使用切换技术以及多Lyapuriov函数方法．研究一类切换模糊系统的稳定性问题．给出了有连续控制输入时该切换模糊系统的一种松弛稳定性条件,避免了并行分配补偿法中固模糊规则数较多而求解公共矩阵P的困难,同时给出了实现系统全局渐近稳定的切换策略．主要条件以LMI的形式给出,具有较强的可解性．空气调节系统的设计实例表明了所提出设计方法的可行性和有效性．     

切换状态反馈控制系统的稳定性分析

研究了一类切换控制系统的稳定性分析问题,切换控制器由多个线性状态反馈控制器组成。运用Lyapunov方法得出了稳定性的时域判据,通过求解一个线性矩阵不等式的方法分析切换控制系统的稳定性,利用KYP引理得到了等价的频域判据;并且研究了一类含有参数不确定性的切换控制系统的鲁棒稳定性分析问题,给出了稳定性时域判据和频域判据。稳定性分析的主要结果是基于公共二次Lyapunov函数的,适用于切换系统任意切换的情形,该方法在工程实例中的应用表明了其有效性。     

Finite-time annular domain stability of impulsive switched systems: mode-dependent parameter approach

This paper investigates the finite-time stability of impulsive switched systems. By applying mode-dependent parameter approach and average impulsive switched interval technique, the conditions that guarantee the finite-time annular domain stability and finite-time annular domain boundedness for general linear and nonlinear impulsive switched systems are established. Meanwhile, the superiority of mode-dependent parameter approach over common parameter approach is analysed. Also, we consider the effect of different impulsive strengths and draw a less conservative conclusion. Moreover, we extend the conclusion from nonlinear impulsive switched systems to linear impulsive switched systems, and a new sufficient condition for state feedback controllers is proposed on the basis of coupled matrix inequalities. Furthermore, for systems containing external disturbance, we obtain a sufficient condition of finite-time annular domain boundedness. Finally, we present two examples to illustrate the effectiveness of the results.     

离散时间两层切换系统的鲁棒指数几乎处处稳定性

提出了一种新类型的切换系统——两层切换系统(Two-level switched systems, TSSs),其顶层切换是确定的,底层切换为随机的且由多个Markov链支配.基于持续驻留时间(Persistent dwell-time, PDT)方法,研究了TSS存在参数不确定性情况下的鲁棒指数几乎处处(Exponential almost sure, EAS)稳定性,以线性矩阵不等式(Linear matrix inequality, LMI)形式给出了一个充分条件.最后通过数值仿真例子验证了本文方法的有效性.     

Stability analysis and stabilization control of multi-variable switched stochastic systems

In this paper, the mean square (MS) stability and exponential mean square (EMS) stability of multi-variable switched stochastic systems are investigated. Based on the concept of the average dwell-time and the ratio of the total time running on all unstable subsystems to the total time running on all stable subsystems, some sufficient conditions are given to ensure the MS stability and EMS stability of the switched stochastic systems involved. Further, for the switched stochastic control systems with all subsystems controllable or stabilizable, EMS stabilization controls and sufficient conditions on EMS stabilization are presented, and the convergent rates of the closed-loop systems are obtained.     

Stability analysis for a class of switched linear systems

This paper investigates the stability of a class of switched linear systems, and proposes a number of new results on the stability analysis. A novel analysis method is developed by using the 2‐norm technique, and then several stability results are obtained based on the new analysis method. It is shown that the main results obtained in this paper not only guarantee the stability of the systems under arbitrary switching, but also provide an algorithm to find the minimum dwell time (MDT) with which switches make the switched systems stable. Finally, several illustrative examples with numerical simulations are studied by using the results obtained in this paper. The study of examples shows that our analysis method works very well in analyzing the stability of some classes of switched linear systems and, moreover, it has some advantages over the common quadratic Lyapunov function method in some cases. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

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.     

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.     

Exponential stability of impulsive positive switched systems with discrete and distributed time‐varying delays

This paper studies the exponential stability problems of discrete‐time and continuous‐time impulsive positive switched systems with mixed (discrete and distributed) time‐varying delays, respectively. By constructing novel copositive Lyapunov‐Krasovskii functionals and using the average dwell time technique, delay‐dependent sufficient conditions for the solvability of considered problems are given in terms of fairly simple linear matrix inequalities. Compared with the most existing results, by introducing an extra real vector, restrictive conditions on derivative of the time‐varying delays (less than 1) are relaxed, thus the obtained improved stability criteria can deal with a wider class of continuous‐time positive switched systems with time‐varying delays. Finally, two simple examples are provided to verify the validity of theoretical results.     

Event-triggered control for switched delay systems with dynamic input quantization

This paper is concerned with event-triggered control for the switched system with time-varying delay and dynamic input quantization. The work is aimed at solving the quantizer saturation in the finite-level quantized control design and the mismatch caused by event-triggered sampling and the switching. First of all, the quantization parameter updating laws are designed respectively in the case of match and mismatch between the system and the controller under the event-triggered mechanism without Zeno behavior. Then, the total variation of Lyapunov functional is transformed into discrete time updating of the dynamic quantization parameter. A switching law and a quantized control strategy are developed to ensure the exponential stability of switched systems with delay and input quantization. At last, two examples are given to illustrate the validity of the results.     

Caputo分数阶切换线性系统的指数稳定性

众所周知,与整数阶切换系统不同, Caputo分数阶切换系统的积分下界不能随子系统的切换而被更新,意味着在下界非一致的任意区间内不能直接取分数阶导数的分数阶积分.对此,本文给出了一个不等式(文中引理6)克服这一问题,并用1个数值例子进行了验证.通过这一不等式,然后分别利用多Lyapunov函数方法和模型依赖平均驻留时间(MDADT)方法,给出了Caputo分数阶切换线性系统指数稳定的条件,并利用2个数值例子进行验证.