基于观测器的不确定离散变时滞系统的稳定性

Stability of Observer-Based Uncertain Discrete Systems with Time-Varying Delays

本文讨论了基于观测器的不确定离散变时滞系统的滑模控制问题。首先,为了估计所要研究的不确定离散系统的状态,构造了状态观测器,并设计了理想的滑模控制律,以保证切换面有限时间的可达性,实现滑动模运动。其次,基于Lyapunov-Krasovskii泛函法以及线性矩阵不等式(LMI)等方法,给出误差离散系统和滑模动力离散方程的渐近稳定性判据。最后,给出了一个数值算例说明了本文结果的有效性和可行性。

In this paper,a sliding mode control problem is concerned for uncertain time-varying delay discrete system with unknown nonlinear function.Firstly,a new observer is constructed to estimate the state of discrete systems,a nonlinear switching function is defined based on the observer and a sliding mode control law is designed to guarantee the reach-ability of the switching surface in a finite time interval.Secondly,based on the Lyapunov functional method,sufficient condition on asymptotic stability of the error system and sliding mode dynamics discrete function are presented in terms of linear matrix inequality(LMI).Finally,a numerical example is provided to demonstrate the effectiveness and feasibility of the proposed results.