Simultaneous stabilization for a collection of single-input nonlinear systems

This paper presents a novel method for designing a controller that simultaneously stabilizes a collection of single-input nonlinear systems. The control Lyapunov function approach is used to derive necessary and sufficient conditions for the existence of time-invariant simultaneously stabilizing state feedback controllers. Additionally, a universal formula for constructing a continuous simultaneously stabilizing controller when the provided sufficient condition is satisfied is presented. For any collection of second-order (and third-order) feedback linearizable systems in canonical form, global simultaneous stabilization via a single state feedback controller is shown to be always possible. Two examples are included for illustration.     

一类不确定非线性切换系统的鲁棒容错控制

研究一类不确定非线性切换系统的鲁棒容错控制问题,当执行器失效或部分失效时,利用Lyapunov函数法建立切换闭环系统混杂状态反馈容错控制器存在的充分条件;然后运用线性矩阵不等式将鲁棒容错控制器设计问题转化为一组线性矩阵不等式的可行解问题,从而借助Matlab中线性矩阵不等式工具箱求解;最后通过数值算倒验证了所提出设计方法的有效性.     

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.     

Feedback Stabilization for Multiinput Switched Nonlinear Systems: Two Subsystems Case

In this note, based on the control Lyapunov function approach, a new method for solving the feedback stabilization problem of switched systems that are switching arbitrarily between two multiinput nonlinear subsystems is introduced. Necessary and sufficient conditions for the existence of globally uniformly asymptotically stabilizing state feedback controllers are derived. Additionally, a universal formula for constructing implementable stabilizing controllers is given when the presented conditions hold. One numerical example is given to illustrate the results.     

Continuous simultaneous stabilization of single‐input nonlinear stochastic systems

This paper investigates the simultaneous stabilization of a collection of continuous single‐input non‐linear stochastic systems, with coefficients that are not necessarily locally Lipschitz. A sufficient condition for the existence of a continuous simultaneously stabilizing feedback control is proposed — it is based on the generalized stochastic Lyapunov theorem and on the technique of stochastic control Lyapunov functions. This condition is also necessary, provided that the system's coefficients satisfy some regularity conditions. Moreover, the proposed feedback can be chosen to be bounded under the assumption that appropriate control Lyapunov functions are known. All the proposed simultaneously stabilizing state feedback controllers are explicitly constructed. Finally, two simulation examples are provided to demonstrate the effectiveness of the proposed approach.     

一类非线性不确定时滞系统的混杂状态反馈H∞鲁棒控制

利用混杂状态反馈控制策略研究一类非线性不确定时滞系统的H∞鲁棒控制问题.假定在给定的控制器集合中有有限个备选的状态反馈控制器,并且每个单一的连续控制器都不能使系统具有鲁棒H∞性能.当控制器的增益矩阵已知时,基于单Lyapunov函数技术和凸组合条件给出控制器切换方案以确保非线性不确定时滞系统具有鲁棒H∞性能.当控制器的增益矩阵未知时,使用多Lyapunov函数技术得到了问题可解的另一个充分条件,同时还给出了混杂状态反馈H∞控制器的设计.     

基于区域极点约束的鲁棒H2控制

考虑了在区域极点约束下状态反馈的鲁棒H2控制问题.分别对含多面体不确定性的连 续和离散系统进行了讨论.基于LMI,给出了存在参数相关的Lyapunov矩阵的充分条件.利用 LMI凸优化方法的解,所得静态反馈控制器,不仅保证闭环系统的极点在-给定区域内,而且还 使性能指标H2的一上界达到最小.     

Simultaneous stabilization of a collection of single‐input nonlinear systems based on CLFs

This paper considers the simultaneous stabilization problem of a collection of single‐input nonlinear systems. Based on the technique of control Lyapunov functions (CLFs), a sufficient condition for the existence of a simultaneously stabilizing state feedback controller is proposed. It is shown that a collection of feedback linearizable systems in canonical form can be simultaneously globally asymptotically stabilized by a single state feedback controller. Moveover, for a set of three‐order chaotic dynamical systems, the simultaneous stabilization problem is considered and a similar result is derived. All the proposed simultaneously stabilizing state feedback controllers are explicitly constructed. Numerical examples are provided to illustrate the effectiveness of the proposed schemes. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

不确定离散线性系统的鲁棒镇定

针对一类具有范数有界时变不确定性的离散性线系统,研究其二次稳定化状态反馈控制律的设计问题。推导出二次稳定化控制律存在一个充分必要条件,该条件被塌一步等价地表示成一个线性矩阵不等式的可解性问题。后者可用现有方法方便地求解,且它的解提供了所有二次稳定定化控制律的一个参数化表示。     

切换时滞线性系统的状态反馈H∞控制

研究一类由任意有限个时滞线性子系统组成的切换系统的状态反馈 控制问题。利用Lyapunov函数方法和凸组合技术,给出由矩阵不等式表示的控制器存在的充分条件,设计相应的子控制器和切换规则。采用变量替代方法,将该矩阵不等式转化为一组线性矩阵不等式。给出一个求解状态反馈控制器增益矩阵的仿真算例。     

一类不确定切换系统的鲁棒状态反馈镇定

研究了一类扰动项不满足匹配条件的不确定切换系统的鲁棒镇定问题.在每个子系统均不能镇定的情况下,利用完备性条件和多李雅普诺夫函数方法,分别得到了不确定切换系统可镇定的充分条件.状态矩阵和控制输入矩阵同时带有时变、未知且有界的不确定性,基于凸组合技术和LMI方法,设计出鲁棒状态反馈控制器及相应的切换策略,使得闭环系统在其平衡点处是渐近稳定的.最后仿真结果表明所设计的控制器及切换策略的正确有效性.     

不确定离散切换系统具有极点约束的保性能控制

对一类含有范数有界不确定性的离散切换系统和一个二次型性能指标，研究其具有闭环极点约束的鲁棒状态反馈保性能控制问题．利用二次Lyapunov函数方法和线性矩阵不等式技术，给出了鲁棒保性能控制器存在的一个充分条件，在所构造切换规则下，闭环系统二次D稳定，且满足给定的性能指标．在此基础上，将次优保性能控制器设计问题转化为一组线性矩阵不等式约束下的凸优化问题．数值例子说明了所提方法的有效性．     

变时滞T-S模糊系统的L∞静态输出反馈控制

针对一类具有状态变时滞的 T-S 模糊非线性系统, 通过定义一类时滞相关 Lyapunov 函数, 引入基于 L∞ 范数理论的鲁棒性能指标, 并利用线性矩阵不等式(LMI), 给出了模糊鲁棒输出反馈控制器的设计方法和存在的充分条件, 保证整个闭环系统的渐近稳定性. 最后, 倒车控制系统的仿真表明了本方法的有效性.     

不确定时滞线性离散切换系统的鲁棒H∞控制

研究一类具有不确定和时滞的线性离散切换系统的鲁棒H∞控制问题．利用多Lyapunov函数技术,在基于状态的切换规则下,给出了这类系统鲁棒镇定且具有H∞性能界的充分条件,以及切换规则和鲁棒H∞切换控制器的设计方案．并将结果应用到一类非切换系统,提出了切换状态反馈控制策略．最后的仿真例子进一步表明了本文结论的有效性．     

不确定广义大系统有限时间鲁棒分散控制

研究不确定连续广义大系统的有限时间鲁棒分散控制问题,设计系统的有限时间鲁棒分散状态反馈控制器.首先应用广义Lyapunov 函数法,给出不确定广义大系统有限时间鲁棒稳定的充分条件;其次,给出不确定广义大系统应用分散状态反馈控制器鲁棒镇定的充分条件和有限时间鲁棒分散控制器的设计方法;最后,通过仿真例子验证所提出方法的有效性.     

一类离散时间切换混杂系统鲁棒控制

由于切换规则的存在使得切换混杂控制系统的稳定性研究变得极为复杂,如何针对给定的系统设计适当的控制器和切换规则没有统一的方法.本文考虑一类线性不确定离散时间切换混杂系统的鲁棒二次镇定和渐近镇定问题.利用公共李雅普诺夫函数方法和多李雅普诺夫函数方法,分别设计了切换混杂系统鲁棒状态反馈控制器和鲁棒输出反馈控制器,保证了切换混杂系统的二次稳定性和渐近稳定性.仿真结果验证了所提算法的正确有效性.     

变时滞不确定关联系统的分散鲁棒无记忆控制

针对一类不确定项具有数值界的变时滞不确定关联系统,主要运用线性矩阵不等式（LMI）方法对其分散鲁棒无记忆控制问题进行了研究,首先,通过构建适当形式的Lyapunov泛函数,运用LMI方法与矢量不等式方法,提出了以一组LMIs有解作为系统可分散鲁棒无记忆控制的充分条件,并给出了系统在此条件下的控制律,然后,将求解一个具有LMIs约束的凸优化问题作为设计尽可能小反馈增益的分散鲁棒无记忆控制律的系统化方法,从而可以得到更符合实际的满意的分散无记忆控制律。     

Decentralized compensation of controller uncertainty in the steady‐state bumpless transfer under the state/output feedback

The state/output feedback topology required for bumpless transfer under controller uncertainty is considered. A steady‐state diagonal dominance condition for a subsystem of this topology is derived, which is shown to be sufficient for the existence of the stabilizing decentralized mismatch compensator parameters. Recent results on the input/output steady‐state gain structure of the one‐degree‐of‐freedom and the two‐degrees‐of‐freedom infinite horizon LQ bumpless transfer topologies are used to show that the diagonal dominance condition applies to topologies generated by a broad class of controllers, thus completing the state/output feedback bumpless transfer technique. The topologies are also shown to be robust with respect to uncertainty in the mismatch compensator. Copyright © 2008 John Wiley & Sons, Ltd.     

广义不确定周期时变系统的鲁棒稳定性分析

研究广义不确定周期时变系统的鲁棒稳定性问题.基于广义周期时变系统Lyapunov不等式,提出了广义不确定周期时变系统鲁棒稳定的概念,采用矩阵不等式(LMI)方法,得到了该类系统鲁棒稳定的充分必要条件;然后,进一步研究了在状态反馈控制下保证闭环系统鲁棒稳定的条件,给出了一族状态反馈鲁棒稳定器的设计方法;最后,引入了广义周期时变系统二次稳定的概念,并讨论了二次稳定性与鲁棒稳定性之间的关系.     

New Results on Stabilization of Fractional‐Order Nonlinear Systems via an LMI Approach

This paper considers the systematic design of robust stabilizing state feedback controllers for fractional‐order nonlinear systems. By using the Lyapunov direct method and a recent result on the Caputo fractional derivative of a quadratic function, stabilizability conditions expressed in terms of linear matrix inequalities are derived. The controllers can then be derived by using existing computationally effective convex algorithms. Two numerical examples with simulation results are provided to demonstrate the effectiveness of our results.