【作者】 李纹；

【导师】 包俊东；

【作者基本信息】 内蒙古师范大学 ， 运筹学与控制论， 2010， 硕士

【摘要】 切换系统是一类重要的混杂系统,它由多个子系统以及作用在其中的切换规则构成。由于切换系统具有广泛的实际应用背景,所以对它的理论研究具有深远的意义。本文研究了几类时滞切换系统的稳定与控制,主要工作如下:(1)针对具有时变时滞的线性切换系统,在控制输入和状态都具有时滞的情况下,研究这类系统的鲁棒H∞控制问题。(2)利用积分不等式和引入自由权矩阵的方法,研究一类不确定变时滞切换系统的鲁棒H∞控制问题。此方法只要求时滞函数上方有界,不需要时滞函数的导数信息。(3)研究一类具有不确定和多时滞的线性离散切换系统的鲁棒H∞问题。基于多Lyapunov函数法,以线性矩阵不等式形式给出了在任意切换信号作用下离散时滞切换系统具有H∞性能的充分条件,同时给出了切换系统有记忆状态反馈H∞控制设计的一种方案。(4)研究了一类具有不确定性并带有中立型时滞的线性切换系统的鲁棒H∞控制问题。利用Lyapunov稳定理论和线性矩阵不等式理论,给出了系统满足H∞性能充分条件,并设计线性有记忆反馈控制器以及切换策略。(5)针对一类由任意有限多个时滞奇异子系统组成的切换系统,研究系统的状态反馈H∞控制问题,利用Lyapunov函数方法和凸组合技术。以LMI的形式给出了在切换状态反馈控制策略下,系统实现状态反馈H∞控制的充分条件。进而给出了切换律和状态反馈H∞切换控制器的设计方案。仿真算例说明控制器设计方案的可行性与有效性。更多还原

【Abstract】 Switched systems are one kind of the important classes of hybrid systems, which consist of a lot of subsystems and switching sequence. There is great signification in theoretical study because of a lot of application in engineering. Stability and H∞control for classes of switched systems are discussed. The main contributions of this paper are as follows.(1) The robust H∞control problem for a class of switched linear systems with time delayed states and inputs is discussed.(2) To uncertain time-varying linear switched systems, the problem of robust H∞controller design is studied by using integral inequality and free-weighting matrix method. It depends on size of delay and requires no information about the derivate of time-delay.(3) The analysis and synthesis of H∞control via state feedback for discrete switched systems with multiple time delay subsystems are studied. Based on multiple Lyapunov functions theory, a new sufficient condition in form of LMI is derived for the H∞performance analysis under arbitrary switching. the robust state-feedback memory controllers are designed(4) Robust H∞feedback for a class of switched systems with uncertainties and neutral time-delays is considered . The systems contain uncertainties not only in the state matrices, but also in the time-delay matrices. Based on Lyapunov theory and linear matrix inequalities, the robust state-feedback memory controllers are designed. With the given switching laws, the controllers can guarantee that the states of systems are robust stable.(5) The state feedback H∞control problem for switched singular systems with delays in both state and control is researched. Based on Lyapunov function approaches and convex combinations techniques, a LMI-based sufficient condition is given for the system implementation of state feedback H∞control .Furthermore, switching law and state feedback H∞controller are designed. A simulation example illustrates the feasibility and effectiveness of the designed controller.更多还原