具有变时滞摄动混杂系统稳定性的研究

研究了一类带有变时滞摄动的混杂系统的稳定性，不要求混杂系统的各个子系统都稳定，但要求每个子系统的摄动矩阵是有界的．分别利用单李雅普诺夫函数和多李雅普诺夫函数方法给出了使混杂系统渐近稳定的条件以及切换律的设计方法，并且基于单李雅普诺夫函数法的设计方法可表示为线性矩阵不等式的形式，给出了相应的基于线性矩阵不等式算法的混杂系统稳定边界的确定方法．最后通过包括两个子系统组成的7昆杂系统进行仿真，而且这两个子系统若作为系统单独运行时都不稳定，但是仿真结果表明利用所提出的方法可使得混杂系统稳定，验证了所提出的方法的有效性．

Stability of hybrid systems with time-varying delayed perturbations

For a class of hybrid systems with time varying delayed perturbations in the time delayed state, two design methods of the switch laws based on Single Lyapunov Function and Multiple Lyapunov Functions were presented to ensure the asymptotic stability of the hybrid system. The subsystem of the hybrid system need not be stable, but the perturbation matrix of each subsystem must be bounded. The method based on single Lyapunov Function can be expressed as Linear Matrix Inequalities (LMIs) that can be solved easily by the tools, such as the LMI toolbox of Matlab. The corresponding LMI based algorithms for determining stability bounds were derived. The example, including two subsystems which were not stable when they run separately, was given to demonstrate the effectiveness of the approaches.