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针对一类含有变时滞和非匹配不确定参数的随机广义Markovian跳系统,提出一种滑模控制的方案。首先构造不带跳变的切换函数,利用线性矩阵不等式给出该系统随机鲁棒渐近稳定的充分条件;然后,为使闭环系统的状态轨迹在有限时间内到达切换面,利用Lyapunov稳定性方法设计了滑模控制器及切换规则;最终使闭环系统产生稳定的滑动模态。数值算例验证了该方法的有效性和可行性。
For a class of stochastic generalized Markovian systems with variable delays and non-matching uncertain parameters, a sliding mode control scheme is proposed. Firstly, the transition function without jumps is constructed and the sufficient conditions for the system to be robustly asymptotically stable are given by using the linear matrix inequalities. Then, to make the state trajectory of the closed-loop system reach the switching surface in a finite time, the Lyapunov stability method The sliding mode controller and the switching rule are designed. Finally, the closed-loop system produces a stable sliding mode. Numerical examples demonstrate the effectiveness and feasibility of the proposed method.