【作者】 熊良林；

【导师】 钟守铭；

【作者基本信息】 电子科技大学 ， 应用数学， 2009， 博士

【摘要】 本论文集中研究中立型系统及切换中立型系统的主要动力学性质,并对其中一些热点子领域中的相关问题进行深入地讨论,得到比较完善而重要的结果.介绍中立型系统及切换中立型系统的研究背景和研究现状,提供论文中常用的基本概念,基础知识和重要引理.它们是后续章节讨论的前提.研究含有分布时滞的中立型系统(包括单分布的中立型系统和多分布时滞的中立型系统两种情形)的渐近稳定性.通过构造新的李雅谱诺夫泛函,结合矩阵分解的技巧和自由矩阵的思想方法,得到保守性较低的时滞相关的稳定性结果.数值实例验证所得结果的有效性和优越性.研究含有非线性扰动的中立型时滞系统的渐近稳定性问题.通过构造新的扩展李雅谱诺夫泛函,结合自由矩阵的思想,并合理利用Schur补引理,得到保守性较低的时滞依赖的稳定性结论.研究含有多时滞的中立型系统的有界输入有界输出稳定性问题.利用等价描述系统的方法,在构造李雅谱诺夫泛函过程中适当引入自由矩阵,结合矩阵分析技巧设计使得系统有界输入有界输出稳定的控制器.讨论切换中立型系统的稳定性分析.首先,提供构造新的分段李雅普诺夫泛函,设计两种使得切换中立型系统稳定的切换规则.其中,依赖于状态的切换规则是通过求解李雅普诺夫-梅兹勒矩阵不等式而设计的,而依赖于时间的切换规则是利用平均驻留时间的方法,并结合线性矩阵不等式求解而得到的.依赖于状态的切换规则降低了现有文献设计的切换规则所带来的保守性.类似地,设计使得切换中立型扰动系统渐近稳定的切换规则.然后,分别利用单李雅谱诺夫泛函和多李雅谱诺夫泛函方法,讨论不同情形下的中立型切换控制系统的稳定性,并设计控制器.其次,利用驻留时间方法讨论包含稳定和不稳定子系统的切换中立型系统,设计使得系统指数稳定的依赖于时间的切换规则.研究不确定性切换中立型控制系统的有界输入有界输出稳定性.其中的不确定性结构为分式不确定性结构,它包括范数有界不确定性.首先结合中立型系统和切换系统的内在性质,得到一般线性切换中立型系统的常数变易公式.然后,结合得到的常数变易公式和自由矩阵的思想,利用驻留时间的方法,得到以线性矩阵不等式表示的稳定性条件.最后,数值仿真验证所得结果的优越性.对全文进行总结,并指出今后的研究方向.更多还原

【Abstract】 Addressed in this dissertation is the key dynamics of neutral systems and switchedneutral systems. Several relevant problems attracting more and more attention in this fieldare discussed in detail, and a series of well-established, systematical, and important re-sults is obtained.The backgrounds and research status of neutral systems and switched neutral sys-tems are introduced. It also provides the readers with some preliminaries and importantdefinitions and lemmas that are frequently used in the remaining chapters.The robust stability for uncertain linear neutral systems with discrete and distributeddelays(the single time delay and multiple time delay are included) is studied. The uncer-tainties under consideration are norm bounded, and possibly time varying. Some noveldelay-dependent stability criteria are derived and formulated in the form of linear matrixinequalities (LMIs) by a new class of Lyapunov-Krasovskii functionals which is con-structed based on the descriptor model of the system and the method of decomposition.The new criteria are less conservative than the existing ones. The examples are suppliedto illustrate the effectiveness of the results presented in this chapter.The asymptotical stability of neutral systems with nonlinear perturbations is studied.Some novel delay-dependent asymptotical stability criteria are formulated in terms of lin-ear matrix inequalities (LMIs). The resulting delay-dependent stability criteria are lessconservative than the previous ones owing to the introduction of free-weighting matricesand the Schur’s lemma, based on a class of novel augment Lyapunov functionals.The delay-dependent bound input bound output(BIBO) stabilization of neutral sys-tems with multiple delays is investigated. Using the method of the descriptor modeltransformation, introducing the free-weighting matrices in the new class of Lyapunov-Krasoviskii functionals, and combining with the matrix analysis technique, the controllerwhich make the systems (BIBO) stable is designed.The stability analysis for the switched neutral systems is considered. First, wepresent new classes of piecewise Lyapunov functionals and multiple Lyapunov function-als, based on which, two new switching rules are introduced to stabilize the neutral sys-tems. One switching rule is designed from the solution of the so-called Lyapunov-Metzler linear matrix inequalities. The other is based on the determination of average dwell timecomputed from a new class of linear matrix inequalities (LMIs). The state-dependentswitching rule is less conservative than the existing results. Similarly, we also analyze thestability of switched neutral systems with nonlinear perturbations. Second, in differentcase, using singular Lyapunov functional and multiple Lyapunov functional respectively,the stabilization for linear uncertain neutral systems with delay in switched control in-put is investigated, and the controller is designed. Third, Based on multiple Lyapunovfunctional approach and dwell-time technique, the stability of the switched neutral sys-tems which both contain the stable subsystems and unstable subsystems is considered.The switching rule which make the switched systems exponential stable is designed. It isshown that by suitably controlling the switching between the stable and unstable modes,the robust stabilization of the switched uncertain neutral systems can be achieved.The problem of delay-dependent bounded input bounded output (BIBO) stability fora class of switched uncertain neutral systems is studied. The uncertainty is assumed tobe of structured linear fractional from which includes the norm bounded uncertainty as aspecial case. First, by introducing the general variation-of-constants formula of neutralsystems with perturbation, the BIBO stability property of general linear switched neutralsystems with perturbation is established. Next, based on the dwell time approach, andcombined with the introduced free-weighting matrices, the BIBO stability criteria are ob-tained in terms of linear matrix inequalities(LMIs). Finally, the simulation examples aregiven to demonstrate the effectiveness and the potential of the proposed techniques in thischapter.We summarize the main results obtained in this dissertation, and point out the futureworks that have been the author’s concerns.更多还原