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

This paper enhances the looped-functional framework for sampled-data systems by using continuous Lyapunov functionals instead of x T ( t ) P x ( t ). The continuous Lyapunov functionals exploit the maximum allowable sampling interval compared with the traditional Lyapunov function x T ( t ) P x ( t ) in the conventional looped-functional framework. The enhanced looped-functional framework ensures the negativeness of the continuous Lyapunov 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 = t k +1 . Also, this paper proposes the stability criteria based on the enhanced looped-functional framework for the sampleddata systems with the asynchronous and synchronous samplings, respectively. The numerical examples show the effectiveness of the proposed framework.