广义受限系统的分析与优化设计

项目名称： 广义受限系统的分析与优化设计

项目编号： No.61074089

项目类型： 面上项目

立项/批准年度： 2011

项目学科： 金属学与金属工艺

项目作者： 左志强

作者单位： 天津大学

项目金额： 10万元

中文摘要： 首先研究了执行器受到饱和非线性限制时马尔科夫跳变系统在转移概率部分未知情况下的随机镇定和H∞#25511;制问题。转移概率部分未知是较转移概率完全已知与转移概率完全未知更具广泛意义和一般性的模型。对于连续系统，我们首先采用固定权的方法，得到了保证闭环系统随机稳定的条件以及均方意义下系统的吸引域。在此基础上，通过引入自由权矩阵进一步降低了结果的保守性，扩大了均方意义下的吸引域范围。针对离散系统，采用类似的思想研究了系统的随机稳定和镇定问题。进而把上述结果推广到了鲁棒H∞#25511;制器的设计，保证闭环系统不仅是随机稳定的，同时外界干扰对系统可调输出的影响限制在一定的范围内。 然后研究了同时具有离散型与分布型不确定时滞系统输入幅值受到限制情形下的可达集估计，其中不确定性是凸多面体形式的。目前已有的结果都是讨论离散型时滞系统的可达集，而许多实际的系统不可避免的存在分布型时滞，分布型时滞的引入使得原有处理离散型时滞系统可达集估计的方法不再适用。我们在选取Lyapunov-Krasovskii泛函引入了包含时间的指数项，并且在求导过程中把最终结果写成具有分布型时滞积分项的形式，从而得到了易于求解的矩阵不等式条件。

中文关键词： 饱和受限；马尔科夫跳变系统；可达集估计;离散型和分布型时滞

英文摘要： The problems of stochastic stabilization and H∞control for Markov jump systems (MJS) subject to partial information on transition probabilities and saturation constraint are firstly studied. The model for MJS with partial information on transition probabilities is more general than the models with completely known and completely unknown transition probabilities. For the continuous-time system, the fixed-weighting matrix approach is used to ensure the stochastic stability of the closed-loop systems and obtain the domain of attraction in mean square sense. Based on it, we derive a less conservative result resorting to the free-weighting matrix way to enlarge the domain of attraction. For the discrete-time case, a similar method is used for stochastic stability analysis and synthesis. In addition, the robust H∞controller is designed to guarantee both stochastic stability and H∞performance of the regulated output in terms of external disturbances. The reachable set estimation for uncertain systems in the presence of both discrete and distributed delays is then considered. The uncertainty is of the polytopic form and the inputs are constrained with peak values. The existing results on reachable set bounding for systems are focused on discrete delays. However, the distributed delays are inevitable for many pratical systems. The introduction of distributed delays makes the traditional method concerning systems with discrete delays no longer applicable. The exponential terms including the time information are involved in the choice of Lyapunov-Krasovskii functional. Moreover, the final result in derivation process is expressed in the form of integral with distributed delay. As a sequence, a matrix inequality criterion is estabilished which can be solved easily.

英文关键词： saturation constraint; Markov jump systems; reachable set estimation; discrete and distributed delay