针对一类分布时滞系统,研究了自适应滑模控制问题。根据分布时滞的特点,构造了适当的Lyapunov泛函,采用线性矩阵不等式方法给出了闭环系统渐近稳定的充分条件。构造了自适应滑模控制器,使系统满足滑模到达条件。设计了时滞独立的积分滑模面并简化了滑模控制器的设计。仿真算例验证了方法的有效性。

Based on a class of distributed delay systems, an adaptive sliding mode controller is proposed. According to the distributed delays, a suitable Lyapunov-Krasovskii functional is constructed, and the sufficient conditions of the asymptotical stability of the closed-loop systems are expressed in linear matrix inequalities. The adaptive sliding mode controller is constructed to satisfy the sliding mode reaching conditions. The delay-independent integral sliding mode is obtained and the sliding mode controller is simplified by the method. A numerical example is given to illustrate the validity of the proposed method.