An enhanced looped-functional framework for stability analysis of sampled-data systems

Abstract

This paper enhances the looped-functional framework for sampled-data systems by using continuous Lyapunov functionals instead of xT(t)Px(t). The continuous Lyapunov functionals exploit the maximum allowable sampling interval compared with the traditional Lyapunov function xT(t)Px(t) in the conventional looped-functional framework. The enhanced looped-functional framework ensures the negativeness of the continuous Laypunov functionals concerning the sampling instants and guarantees the stability of the sampled-data systems. Based on these continuous Lyapunov functionals, this paper constructs novel Lyapunov functionals with the looped-functional which not only exploits all available vectors related to sampling intervals but also introduces an additional interval which is zero at t=tk+1. Also, this paper proposes the stability criteria based on the enhanced looped-functional framework for the sampled-data systems with the asynchronous and synchronous samplings, respectively. The numerical examples show the effectiveness of the proposed framework.