Robust Impulsive Stability for Uncertain Linear Discrete-Time Systems with Delay

Abstract

研究了一类范数有界的不确定线性离散时滞系统的鲁棒脉冲镇定问题。通过引入与脉冲时间序列相关的时变Lyapunov泛函，利用凸组合技术，以线性矩阵不等式的形式，建立了不确定线性离散脉冲时滞系统的鲁棒指数稳定的判别准则。通过求解线性矩阵不等式，得到鲁棒状态反馈脉冲控制律的增益矩阵。数值实例仿真验证了结果的有效性、可行性。 This paper investigates the problem of robust impulsive stabilization of uncertain linear dis-crete-time systems with delay. By introducing the time-varying Lyapunov function that captures the dynamical characteristic of discrete-time impulsive delayed uncertain linear systems, and utilizes a convex combination technique, new robust exponential stability criteria for uncertain linear discrete-time impulsive delayed systems are established in terms of linear matrix inequalities. And the feedback gain matrices of robust impulsive control law are obtained. Numerical simulations are rendered to exemplify the effectiveness and applicability of the proposed results.