滑模控制一类非线性分布式时滞系统

Sliding mode control for a class of nonlinear systems with distributed delay

针对一类状态不可测的非线性不确定分布式时滞系统,给出了系统滑动模态鲁棒渐近稳定的充分条件.设计了一类滑模观测器,同时采用线性矩阵不等式的处理方法给出了该观测器存在的充分条件.再应用滑模控制的趋近率方法和基于观测器所得到的估计状态,综合了一类滑模控制器.该控制器同时保证了估计状态下的滑模面和估计误差状态下的滑模面的渐近可达性.

The design problems of sliding mode observer and the observer-based controller are addressed for a class of uncertain nonlinear systems with distributed delays. According to the sliding mode control theory, we propose a sufficient condition of robust asymptotic stability for the sliding mode dynamics. A sliding mode observer is designed, and the sufficient condition is given for the existence of such an observer in terms of linear matrix inequality （LMI）. Based on the observed states, a controller is synthesized by using the sliding mode control theory and the reaching law technique. The proposed control scheme guarantees the reachability of the sliding surfaces defined in both the observed state space and the observed state-error space.