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.     

一类切换模糊时滞组合系统的分散镇定

提出了切换模糊时滞组合系统模型,并研究了状态和互联项具有时滞情况下的分散镇定问题.当每个互联子系统中的每个切换子系统具有有限个备选的状态反馈控制器,且单一控制器均不能保证系统稳定的情况下,利用多Lyapunov函数方法给出了时滞相关的矩阵不等式条件和分散切换律设计方法,使系统在所提出的分散切换律和分散控制器下渐近稳定.仿真结果表明了所提出方法的有效性.     

具有时变时滞的离散切换系统基于观测器的H∞控制

利用多Lyapunov函数方法，研究一类具有时变时滞的线性离散切换系统基于观测器的H∞控制问题．通过设计对角分块形式的多Lyapunov函数矩阵．使切换律只依赖于观测状态．在基于观测器的切换反馈控制策略下,给出了系统实现H∞控制的充分条件，且条件可以表示为与时滞界相关的线性矩阵不等式（LMI）的形式．同时还给出了切换律、观测器和控制器的设计方案．最后用一个仿真例子表明了结论的有效性．     

一类多输入级联非线性切换系统的全局镇定

研究一类带有部分线性系统的多输入级联非线性切换系统的全局镇定问题. 首先, 给出保证线性部分有一致规范型的充分条件. 其次, 利用一致规范型及其零动态的共同二次Lyapunov函数设计状态反馈使得线性部分在任意切换律下镇定. 最后, 通过构造共同Lyapunov函数能实现闭环系统在任意切换律下的全局渐近稳定性.     

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.     

一类切换系统极限环的反馈镇定研究

利用多Lyapunov函数法讨论一类切换系统极限环的反馈镇定问题．首先给出切换系统极限环的有界状态反馈、有界输出反馈以及动态反馈镇定定理;然后利用Jurdjevic—Quinn方法给出反馈控制器的具体形式,并证明了在给定反馈控制器的作用下,切换系统的极限环渐近稳定．仿真例子验证了结论的正确性．     

基于反步法的一类非线性切换系统控制器设计

研究一类子系统是纯反馈非线性系统的切换系统控制器设计问题．基于多Lyapunov函数和反步法,提出一种状态反馈控制律及切换规则设计方法。通过递推设计可得到使非线性切换系统稳定的反馈控制律和切换规则．将所提出的方法应用于该类非线性切换系统含有不确定性的情形,仿真算例结果表明了所提出方法的有效性．     

一类切换系统基于观测器的滑模降阶控制

针对一类状态不可测的切换系统, 研究了其基于观测器的滑模控制问题. 设计了一类降阶观测器, 并用观测到的状态设计了滑模面函数以及滑模控制器, 使得闭环系统的状态能够到达滑模面上, 产生滑动模态. 并应用Lyapunov函数的方法给出了切换系统的滑动模态可达条件以及确保闭环切换系统渐近稳定的离散切换律. 最后,数值仿真验证了本文所提方法的有效性.     

具有状态时滞的离散时间切换系统的H∞ 滤波器设计: 依赖状态的切换方法

讨论一类时滞离散时间切换系统的H∞滤波器的设计问题.首先,当所有子系统都稳定时,基于切换Lyapunov函数和Finsler引理,得到了滤波误差系统渐近稳定且具有指定的H∞性能指标的充分条件,即使切换系统的每个子系统均不稳定,通过利用多Lyapunov函数方法和依赖状态的切换技术仍能保证切换系统稳定;然后,设计了H∞滤波器,并得到滤波误差系统满足指定的H∞性能指标的充分条件;最后,通过数值算例验证了所提出方法的有效性.     

一类不确定切换组合系统的分散H∞鲁棒镇定

主要研究一类不确定切换组合系统H∞意义下鲁棒稳定性问题,利用单Lyapunov函数和多Lyapunov函数技术,给出了使这类系统渐近稳定且具有H∞扰动衰减度的两种分散切换律的设计方案.     

Absolute exponential stability and stabilization of switched nonlinear systems

This paper is concerned with the problems of absolute exponential stability and stabilization for a class of switched nonlinear systems whose system matrices are Metzler. Nonlinearity of the systems is constrained in a sector field, which is bounded by two odd symmetric piecewise linear functions. Multiple Lyapunov functions are introduced to deal with the stability of such nonlinear systems. Compared with some existing results obtained by the common Lyapunov function approach in the literature, the conservatism of our results is reduced. All present conditions can be solved by linear programming. Furthermore, the absolute exponential stabilization for the considered systems is designed by the state-feedback and average dwell time switching strategy. Two examples are also given to illustrate the validity of the theoretical findings.     

切换系统不变集的输出反馈镇定

利用一个非负函数V (x), 推广了小时间状态模可观测和大时间状态模可观测的定义, 提出了小时间V (x)可观测和大时间V (x)可观测的概念. 利用V (x)可观测的概念, 讨论了子系统无源的切换系统不变集的有界输出反馈镇定及动态输出反馈镇定. 利用多Lyapunov函数证明了闭环系统渐近稳定. 仿真例子验证了文中结论正确性.     

Stability of discrete-time switched systems with admissible edge-dependent switching signals

The problem of stability is studied in this paper for a class of discrete-time switched systems with unstable subsystems. Two new definitions of slow switching and fast switching on the basis of admissible edge-dependent average dwell time are proposed, respectively. Some conditions are established by using multiple Lyapunov function method to guarantee the global uniform exponential stability of discrete-time switched systems. Finally, a numerical example is presented to demonstrate the effectiveness of the proposed results.     

Output feedback variable structure control for a class of uncertain switched systems

This paper considers the output feedback variable structure control problem for a class of uncertain switched systems. A single sliding surface is constructed using only output information. Robust stability of the sliding motion restricted to the sliding surface is achieved and complete invariance to the matched and the mismatched uncertainties is guaranteed via a hysteresis switching law based on a reduced order observer. Output feedback variable structure controllers are given to guarantee that the redefined sliding surface is reached in finite time. A numerical example illustrates the effectiveness of the proposed design method. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

一类非线性离散时间系统的模糊辨识

对一类非线性离散时间系统提出了模糊辨识方法,此方法用与未知参数向量成线性关系的模糊逻辑系统作为辨识模型,并通过自适应学习律对此模糊逻辑系统中的未知参数进行自适应调节,文中证明了此方法可使辨识误差收敛到原点的一个邻域内。仿真结果验证了此方法的有效性。     

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．     

Exponential stabilization of discrete-time switched linear systems

This article studies the exponential stabilization problem for discrete-time switched linear systems based on a control-Lyapunov function approach. It is proved that a switched linear system is exponentially stabilizable if and only if there exists a piecewise quadratic control-Lyapunov function. Such a converse control-Lyapunov function theorem justifies many of the earlier synthesis methods that have adopted piecewise quadratic Lyapunov functions for convenience or heuristic reasons. In addition, it is also proved that if a switched linear system is exponentially stabilizable, then it must be stabilizable by a stationary suboptimal policy of a related switched linear-quadratic regulator (LQR) problem. Motivated by some recent results of the switched LQR problem, an efficient algorithm is proposed, which is guaranteed to yield a control-Lyapunov function and a stabilizing policy whenever the system is exponentially stabilizable.     

Adaptive finite-time control for a class of switched nonlinear systems using multiple Lyapunov functions

This paper investigates the problem of global adaptive finite-time stabilisation for a class of switched nonlinearly parameterised systems. Without requiring that each subsystem is globally adaptively finite-time stabilisable, a switched adaptive finite-time control scheme is developed by exploiting the multiple Lyapunov functions method and adding a power integrator technique. By using the parameter separation technique, the unknown parameters are separated from nonlinear functions. On the basis of finite-time Lyapunov stability theory, it is proved that the proposed controller can guarantee that the state of the resulting closed-loop system converges to the origin in finite time. Finally, an example is given to demonstrate the effectiveness of the proposed method.     

Stabilization for nonlinear fractional-order time-varying switched systems

This paper deals with the global asymptotic stabilization problem for discontinuous nonlinear time-varying switched systems in the sense of fractional-order. Via the designed periodic switching law, some criteria are firstly developed. It is shown that the derivatives of the constructed Lyapunov functions are allowed to be indefinite. Several corollaries are further derived, and some existing results can be regarded as special cases of our obtained results. Finally, our findings are verified by three numerical examples and one experiment.