【作者】 宗广灯；

【导师】 武玉强；

【作者基本信息】 东南大学 ， 控制理论与控制工程， 2005， 博士

【摘要】 切换动态系统是一类重要的混合动态系统,它是由几个连续时间子系统或离散时间子系统及作用在其中的切换规则构成的。切换系统不同于一般的连续时间系统或离散时间系统,它具有一些特殊的性质。由于切换的存在使得系统的动态特性变得非常复杂,例如系统的状态轨迹可能会发生跳变,系统的稳定性可能会发生改变。因而,切换规则的选择是非常重要的。在过去三十年中,控制界对切换系统的建模、分析、综合与控制的研究兴趣不断升高。切换系统分析和切换控制的研究越来越受到人们的关注。本文主要讨论线性不确定切换系统、时滞切换系统的反馈控制器设计与切换策略的设计,以及闭环系统的全局渐近稳定性、二次稳定性和指数稳定性。本文的主要研究成果如下:一、研究了一类带有结构扰动的离散时间脉冲切换系统的鲁棒指数稳定性,假定切换系统包含了稳定子系统和不稳定子系统。应用平均驻留时间的概念,通过将切换系统的激励时间划分为稳定子系统的激励时间和不稳定子系统的激励时间,证明了只要切换系统的平均驻留时间以及稳定子系统与不稳定子系统的激励时间之比适当大,所设计的切换机制就可以保证切换系统是鲁棒指数稳定的,并具有期望的稳定裕度。与传统的李雅普诺夫函数方法相比,该设计思路简单、易实现。二、考虑了带有状态跳跃和结构扰动的连续时间切换系统的指数稳定性。给定系统既可以包含稳定子系统又可以包含不稳定子系统。通过将系统总的激励时间划分为两部分,证明了只要系统的平均驻留时间充分大以及带有负测度子系统的激励时间与非负测度子系统的激励时间之比充分大,给定切换系统就是全局指数稳定的,并具有期望的稳定裕度。该部分的主要贡献在于为切换系统的指数稳定性研究提供了一种实际可行的算法。三、分析了带有非线性扰动的离散时间切换系统的鲁棒二次镇定和渐近镇定问题,非线性扰动满足了匹配条件。基于公共李雅普诺夫函数方法和多李雅普诺夫函数方法,分别设计了切换系统鲁棒状态反馈控制器和鲁棒输出反馈控制器,给出了系统渐近镇定切换律的设计,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算法的正确有效性。四、研究了带有结构扰动的线性不确定离散时间切换系统的鲁棒二次镇定和渐近镇定问题。基于李雅普诺夫函数方法,以矩阵不等式的形式给出了切换系统鲁棒状态反馈控制器和鲁棒输出反馈控制器设计,并设计了相应的切换律,保证了闭环切换系统的二次稳定性和渐近稳定性。五、考察了具有结构扰动和非线性干扰的连续时间不确定切换系统的鲁棒状态反馈镇定问题,非线性干扰项包含了满足匹配条件和不满足匹配条件两部分。对于给定的不确定切换系统,研究了其二次镇定和渐近镇定问题。基于李雅普诺夫函数方法,以矩阵不等式的形式给出了切换系统鲁棒状态反馈镇定的若干充分条件。仿真结果表明,该部分的设计方法是有效的。该部分内容是在第三、四部分工作的基础上,所作的进一步研究。六、考虑了一类带有状态时滞和非线性扰动的离散时间切换系统的鲁棒静态输出反馈镇定和动态输出反馈镇定问题。利用Schur补公式和线性矩阵不等式的相关概念,给出了闭环切换系统鲁棒全局一致渐近稳定的一系列充分条件。此外,本章还研究了切换系统渐近稳定时非线性扰动项所应该满足的最大上界,并指出这一问题可以通过判断一个凸优化问题的可解性来解决。所有结果均以线性矩阵不等式的形式给出。该部分设计思路简单、易实现。更多还原

【Abstract】 As an important class of hybrid dynamical systems, a switched system is composed of several continuous-time sub-systems or discrete-time subsystems and the switching signals among them. With its own particularity, it is different form the traditional continuous-time systems or discrete-time systems. Due to the existence of the switching signal, its dynamics may become very complicated, for example, the state trajectory may jump at the switching point, its stability may change. Hence, it is very important to how to choose the proper switching signal. During the last three decades of so, there is an increasing interest on the modeling, analysis, synthesis, and control of witched systems. Nowadays more and more people have paid attention to the stability analysis of the switched systems and the study of the switching control.This dissertation devotes on the study of the linear uncertain switched systems and time-delay systems, including the design of the feedback controllers and the switching signals, the globally asymptotical stability and the exponential stability of the closed-loop systems. The main contributions of the research work presented in this dissertation are as follows:1. In the first part, the robust exponential stability of a class of discrete time impulsive switched systems with structure perturbations is studied. The given switched systems are composed of stable subsystems and unstable subsystems. Based on the average dwell time concept and by dividing the total activation time into the time with stable subsystems and the time with unstable subsystems, it is shown that if the average dwell time and the ratio of the activation time with stable subsystems to the activation time with unstable subsystems are properly large, the given switched system is robustly exponentially stable with a desired stability margin. Compared with the traditional Lyapunov methods, our layout is more clear and easy to carry out.2. In the second part, the exponential stability is considered for continuous time switched systems containing both stable and unstable subsystems with state jump and structure perturbations. By utilizing the matrix measure concept and the average dwell-time approach, it is shown that if the average dwell-time and the ratio of the total activation time of the subsystems with negative matrix measure to the totalactivation time of the subsystems with nonnegative matrix measure are both chosen appropriately large, the exponential stability of a desired degree is guaranteed. The main contribution of this part is that a feasible algorithm on the exponential stability study of the switched systems is proposed.3. In the third part, the robust quadratic stabilization problem and asymptotic stabilization problem are analysized for discrete time switched dynamical systems with nonlinear perturbations, which satisfy the matching condition. The robust state feedback controllers and output feedback controllers are designed respectively using common Lyapunov function technique and multiple Lyapunov function technique. Also the asymptotical stabilization switching laws are presented. The designed controllers and switching signals guarantee the quadratic stability and asymptotic stability.4. In the forth part, we go on studying the robust stabilization problem for discrete time switched systems. Here we consider the stabilization problem of structure perturbed uncertain discrete time switched systems. Robust state feedback controllers and output feedback controllers are designed respectively using common Lyapunov function technique and multiple Lyapunov function technique. Additionally, the asymptotical stabilization switching laws are presented, which guarantee the quadratic stability and asymptotic stability of the closed-loop switched systems.5. In the fifth part, the robust state feedback stabilization problem is investigated for continuous time switched systems with structure perturbations and nonlinear disturbances. The nonlinear disturbances include the uncertainty satisfying matching condition and the one not satisfying the matching condition. The problems of quadratic stabilization and asymptotic stabilization are considered for the given uncertain switched systems. Based on the common Lyapunov function technique, several sufficient conditions for the robust stability of the switched systems are presented in the form of matrix inequalities. The simulations validate the effectiveness of the main algorithm. The work in this part forwards the study in the previous two parts.6. In the sixth part, the robust static output feedback stabilization problem and robust dynamic output feedback stabilization problem are analyzed for a class of discrete-time switched systems with state delays and nonlinear perturbations. By utilizing Schur complement formula and the related notion of LMI, a series of sufficient conditions are presented, which guarantee the robustly globally uniformlyasymptotic stability of the closed-loop switched system. Additionally, the problem of the maximal nonlinear bound when the closed-loop switched system is asymptotically stable is also studied. As we pointed out, this problem can be solved by judging the feasibility of one convex optimization. All the results are given in linear matrix inequality form. The simplicity of the design algorithm makes it easy to carry out.更多还原