含有死区饱和的不确定离散时滞系统的滑模控制

Sliding Mode Control for Uncertain Delay Discrete-time Systems with Dead-zone Saturation

研究了含有死区和输入饱和的不确定离散时滞系统的滑模控制问题,其中参数不确定性同时存在于系统的状态矩阵和控制输入矩阵中.构造了一种拟积分型切换面,可保证系统状态轨迹从开始时刻就位于切换面上.利用李亚普诺夫稳定性理论和线性矩阵不等式技术给出了滑模动态系统渐近稳定的充分条件.而且,所设计的滑模控制律可以保证在死区和饱和影响下的滑动模态仍是可达的.数值仿真验证了本文设计方法的有效性.

The problem of sliding mode control for uncertain delay discrete-time systems with dead zone and input satura- tion is studied. In the systems under consideration, there exist uncertainties both in the state matrix and the input matrix. An integral-like switching surface is chosen such that the trajectories of states will lie on the sliding surface at the initial time. By means of Lyapunov stability theory and linear matrix inequality technique, a sufficient condition is derived to ensure the asymptotic stability of sliding mode dynamics. Furthermore, a new sliding mode controller is designed to ensure the reach- ability of the sliding mode dynamics despite the effects of dead zone and saturation input. Finally, the numerical simulation results show the effectiveness of the proposed method.