不确定时滞系统的滑模控制

Sliding-Mode Control for Uncertain Time-Delay Systems

考虑同时存在状态不确定性和控制不确定性的时滞系统的滑模控制问题,其中控制不确定性是不匹配的。利用Lyapunov方法和线性矩阵不等式技术,给出了闭环系统渐近稳定的充分条件。利用该线性矩阵不等式的解可以得到所设计的滑模控制律和滑模面。从理论上证明了该滑模控制律能保证状态轨迹被驱动到指定的切换面上。仿真结果验证了该算法的有效性。

The problem of sliding-mode control for a class of time-delay systems is considered. There are uncertainties in both state matrices and input matrix. Moreover, the uncertainties in input matrices is mismatched. By using Lyapunov theory, a sufficient condition in terms of linear matrix inequalities （LMIs） is derived such as the asymptotical stability of the closed-loop system is guaranteed. When the LMIs are feasible, the design of both sliding mode control law and sliding surface can be easily obtained via convex optimization. Moreover, state trajectories are attracted onto the specified sliding surface. A simulation is given to illustrate the effectiveness of the proposed method.