基于有限时间的一类时滞非线性切换系统滑模控制

研究一类时滞非线性切换系统的有限时间滑模控制问题.针对所研究的系统模型,构造每个子系统对应的积分滑模面,基于滑模控制理论,设计带有状态时滞的滑模控制器使得每个子系统能在有限时间内到达相应的滑模面上,并对系统中存在的非线性项采用Lipschitz条件进行处理.根据多李亚普诺夫函数、平均驻留时间方法以及分割策略引理,给出滑模趋近段和滑模动态有限时间有界的充分条件,并通过对线性矩阵不等式的求解得到控制器增益.最后,通过一个数值仿真例子验证该设计方法的有效性.

Finite-time sliding mode control for a class of nonlinear and time-delayed switched systems

This paper investigates the problems of finite-time sliding mode control for a class of nonlinear switched systems with time-delays. For the studied system model, the corresponding integral sliding mode surface of each subsystem is constructed. Based on the sliding mode control theory, a sliding mode controller is designed to make every subsystems state be driven onto the relevant sliding mode surface within a given time-interval. And the Lipschitz conditions are used to deal with the nonlinearities in the system. By means of the multiple Lyapunov functions technique, average dwell time approach and partitioning strategy, sufficient conditions are proposed to guarantee the finite-time boundedness of the corresponding sliding mode dynamic systems, and the controller gains is obtained by solving the linear matrix inequalities. Finally, a simulation example is given to illustrate the effectiveness of the proposed methods.