多平衡点二维线性时不变切换系统的稳定性及镇定性

研究含不稳定子系统的多平衡点二维线性时不变切换系统的稳定性和镇定性问题.首先,在每一子系统仅有唯一焦点或中心、不同子系统的平衡点互异的情形下,确定含所有子系统平衡点的唯一特定区域,据此给出系统区域稳定的概念;然后,基于区域稳定的定义,利用解析法得到系统全局区域渐近稳定的简单判据,并设计了全局区域渐近镇定控制器及其算法.最后,通过数值仿真算例表明了所得结果的有效性和易操作性.     

基于最小驻留时间法估计线性切换系统的分量最终界

研究线性切换系统的最终界问题.首先,通过应用最小驻留时间法和分量最终界方法得到线性切换系统的分量最终界;然后,基于2-范数方法得到了估计线性切换系统最小驻留时间的新方法.与已有方法相比,该方法在某些情况下具有一定的优势,减少了估计的保守性.数值仿真结果验证了所得结论的正确性和有效性.     

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.     

一类切换线性广义系统的稳定性

提出了一种新的切换系统即广义切换系统．应用共同Lyapunov函数方法研究切换线性广义系统的稳定性,给出了切换广义系统在任意切换律下都稳定的充分条件．以及构造一类共同Lyapunov函数的方法．最后的数值例子说明了方法的可行性．     

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.     

一类离散线性切换系统的最优控制

研究了一类离散线性切换系统在切换时间、切换次数固定的情况下的二次最优控制问题.利用离散动态规划的方法,将多级决策过程分解成一系列易于求解的单级决策过程,求出最优控制序列和最优切换序列,并给出算法.最后通过一个数值例子来说明所提出的方法的有效性.     

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.     

一类线性切换广义系统的保性能控制

针对一类线性切换广义系统,研究了其在任意切换策略下的保性能控制问题。结合一个二次型性能指标,利用单Lyapunov函数方法和线性矩阵不等式(LMI)技术,给出了状态反馈保性能控制器存在的一个充分条件,使得相应的闭环切换广义系统保持正则、稳定和无脉冲,且闭环性能指标值不超过某个确定上界。并进一步将保性能控制器的设计问题转化为线性矩阵不等式的可行解问题,使得控制器的设计更加简便,易于操作。这个条件可以通过Matlab的LMI工具箱求解,适合在工程中应用。数值仿真例子说明了该方法的有效性。     

一类线性连续切换系统的迭代学习控制

针对有限时间区间内执行重复控制任务的线性连续切换系统,考虑基于迭代学习的跟踪控制问题.假设线性切换系统的切换率在时间域内是任意的,提出该类系统的D型迭代学习控制算法.理论分析表明,当学习增益矩阵满足一定的条件时,D型迭代学习控制算法可以保证切换系统的实际输出在整个运行区间上一致收敛于期望输出,实现完全跟踪控制.数值仿真进一步验证了方法的有效性.     

一类线性不确定切换时滞系统的可靠保成本控制

研究了一类含有故障执行器的线性不确定切换时滞系统的可靠保成本鲁棒控制问题．当执行器发生“严重失效”——未失效执行器不能镇定原系统时,基于多Lyapunov函数的方法,以线性矩阵不等式(LMIs)的形式给出了状态反馈可靠保成本控制器存在的充分条件,同时对于闭环系统的成本函数进行了优化．最后用仿真结果验证了所设计方法的有效性．     

Estimation of stability region for discrete‐time linear positive switched systems with multiple equilibrium points

This paper investigates the regional stability for discrete‐time linear positive switched systems with multiple equilibrium points (PSS‐MEP). Every subsystem possesses a unique stable equilibrium point. Firstly, by establishing a special Lyapunov function, a sufficient condition for region stability of considered systems is presented. Although, estimating the stability region for n‐dimensional PSS‐MEP with l ≥ 3 subsystems is still a challenging work, we study the one and two dimensional PSS‐MEP, and the corresponding accurate stability regions are given in our main job. Finally, a simulation example is presented to demonstrate the correctness of the theoretical results.     

一类线性开关系统的渐近稳定性

研究一类线性开关系统的渐近稳定性问题。针对不满足完备性条件的开关系统 ,利用 L ya-punov函数技术 ,给出了系统渐近稳定的一个充分条件 ,并举例说明了该方法的实际应用     

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.     

时滞切换系统的时滞依赖稳定

首先利用多Lyapunov 函数方法, 分析常时滞切换系统的时滞依赖稳定性, 并给出此系统时滞依赖稳定的充分条件及切换律的设计; 然后运用共同Lyapunov 函数方法, 研究一类时变时滞切换系统的时滞依赖稳定性, 也给出此系统时滞依赖稳定的充分条件及切换律的设计. 所得结果均可用线性矩阵不等式方法求解. 最后通过仿真验证了结论的正确有效性.     

Finite-time stability and stabilisation for switched linear systems

In this article, the finite-time stability analysis and stabilisation for switched continuous linear system are addressed. Several sufficient conditions for finite-time boundness and stability of switched system are proposed in this article. By comparing the proposed results, it is shown that more the information about the switching signal is known, less conservative results can be derived. Then, based on the finite-time stability analysis results, static state and dynamic output feedback controllers are designed to finite-time stabilise switched linear systems. Several numerical examples are given to illustrate the proposed results within this article.     

Stochastic input-to-state stability for impulsive switched stochastic nonlinear systems with multiple jumps

In this study, we investigate the stochastic input-to-state stability (SISS) of impulsive switched stochastic nonlinear systems. In this model, the impulse jumps are component multiple maps that depend on time. Thus the model differs from traditional impulsive systems with single impulse between two adjacent switching times. We provide sufficient conditions in three cases with the SISS system by using the Lyapunov function and average impulsive interval approach. The destabilising impulses cannot destroy the SISS properties if the impulses do not occur too frequently when all the subsystems that control the continuous dynamics are SISS. In other words, the average impulsive interval satisfies a lower bound restraint. Conversely, when all subsystems that control the continuous dynamics are not SISS, impulses can contribute to stabilising the system in the SISS sense when the average impulsive interval satisfies an upper bound. Then, we investigate the SISS property of impulsive switched stochastic nonlinear systems with some subsystems that are not SISS under certain conditions such that the property remains obtained. Finally, we show three examples to demonstrate the validity of the main result.     

Periodically switched stability induces exponential stability of discrete-time linear switched systems in the sense of Markovian probabilities

The conjecture that periodically switched stability implies absolute asymptotic stability of random infinite products of a finite set of square matrices, has recently been disproved under the guise of the finiteness conjecture. In this paper, we show that this conjecture holds in terms of Markovian probabilities. More specifically, let S_k∈C^n×n,1≤k≤K, be arbitrarily given K matrices and , where n,K≥2. Then we study the exponential stability of the following discrete-time switched dynamics S: where can be an arbitrary switching sequence.For a probability row-vector and an irreducible Markov transition matrix with , we denote by the Markovian probability on corresponding to . By using symbolic dynamics and ergodic-theoretic approaches, we show that, if S possesses the periodically switched stability then, (i) it is exponentially stable -almost surely; (ii) the set of stable switching sequences has the same Hausdorff dimension as . Thus, the periodically switched stability of a discrete-time linear switched dynamics implies that the system is exponentially stable for “almost” all switching sequences.     

离散线性开关系统切换的模糊方法

在已知离散线性开关系统全局渐近稳定前提下，将线性开关系统切换问题转化为相应T－S模型模糊区域划分问题，通过在线实时调整T－S模型隶属函数参数来确定模糊区域，以二阶离散线性开关系统为例，给出了实现系统全局渐近稳定的模糊切换策略，该方法可扩展到高阶线性开关系统，计算机仿真证实该方法简捷，有效。     

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