广义马氏跳变系统在一般转移速率下的控制器设计

摘要

针对转移概率不能精确获得并且部分未知的广义马氏跳变系统,分别讨论在模态依赖控制器和模态独立控制器条件下的系统镇定问题。与现有结果相比,所提研究方法具有较小的保守性,能够有效地解决实际问题。首先,运用自由权矩阵方法,得到了广义马氏跳变系统在转移速率满足上述一般条件时系统随机容许的充分条件。在此基础上,以线性矩阵不等式(Linear matrix inequality, LMI)的形式分别给出了模态依赖和模态独立控制器的求解条件。最后,通过数值算例验证设计方法的有效性和优越性。%This paper considers the stabilization of singular Markovian jump systems with general switching, where the tran-sition rate matrix is uncertain and partially unknown. Com-pared with the existing results, the methods proposed in this paper are less conservative and are very suitable to deal with many practical problems. First, a new condition of stochastic admissibility for singular Markovian jump systems with general switching is obtained by exploiting the slack variable method. Then, several conditions for the existence of mode-dependent and mode-independent controllers are developed in terms of lin-ear matrix inequalities (LMIs). Finally, a numerical example is given to show the effectiveness and advantages of the design methods.