离散时变时滞系统的鲁棒稳定性新判据

New robust stability criterion for discrete-time system with time-varying delay

针对具有非线性扰动的离散时变时滞系统的鲁棒稳定性问题,本文利用离散Lyapunov函数方法,构造适当的Lyapunov函数,并借助新提出的求和不等式方法,给出了所讨论系统的鲁棒稳定性新判据。所得结果是时滞相关的,以线性矩阵不等式(LMI)的形式给出,并通过MATLAB的LMI工具箱求解。数值实例验证该结果具有较小的保守性,表明本文所获得的结果具有有效性和优越性。

The robust stability problem is considered for discrete-time systems with time-varying delay and nonlinear perturbation. Based on a proper Lyapunov function and newly proposed summation inequality, a less conservative delay-dependent robust stability criterion is derived in terms of the linear matrix inequality, which could be solved by using LMI tools of MATLAB.Numerical examples are given to demonstrate the less conservativeness and advantages of the proposed method.