异步切换下一类线性时变时滞系统的鲁棒控制

摘要

研究了异步切换下含有不确定的时变时滞线性系统的鲁棒控制问题.利用平均驻留时间方法构造了新的李雅普诺夫泛函以及矩阵不等式, 得到了异步切换下给定系统鲁棒指数稳定的充分条件, 并在此基础上设计了控制器.异步切换是指备选控制器间的切换与系统模型间的切换是异步的, 这是由于系统切换时需要时间识别系统模型并匹配相应的控制器.构建的李雅普诺夫函数由控制器的切换信号决定, 从而能有效地解决控制器的设计问题, 使子系统的运行时间分为两部分:异步阶段以及同步阶段, 李雅普诺夫的函数值在异步阶段是允许增长的.对于得到的系统鲁棒指数稳定的新判据以及相对应的状态反馈控制器, 可以利用MATLAB等数学工具对其进行求解.%In this paper, the robust control problem for the uncertain linear time-varying systems under asynchronous switching is investigated.Based on average dwell time approach and LMIs, choosing the new Lyapunov function and LMIS, the sufficient condition for the robust exponentially stabilizable and the corresponding controller are obtained.The so-called asynchronous switching means that the switching between the candidate controllers and system modes are asynchronous.The reason is that the switching takes time to identify the system modes and apply the matched controllers.The Lyapunov-like function dependent on the controllersswitching signal is constructed, which can effectively counteract difficulty of controller design, however, the running time of the subsystem is divided into two parts:matched periods and mismatched periods, and the value of the Lyapunov function is allowed to increase during the asynchronous phase.For the criterion that the given system is robust exponentially stabilizable and the state-feedback controller under asynchronous switching, they can be solved easily by using MATLAB tools.