A less conservative stability criterion for sampled-data system via a fractional-delayed state and its state-space model

Abstract

This paper introduces a state-space model based on a fractional-delayed state for a sampled-data system described as a linear system under aperiodic sampling intervals. The new state-space model exploits the information on the sampled-data system and the fractional-delayed state, which is defined on the sampling interval. The fractional-delayed state and its state-space model are utilized to construct the Lyapunov functional, which consists of the traditional Lyapunov function and a looped functional whose boundary conditions are zeros at sampling instants. Based on the Lyapunov functional, a stability criterion and a robust stability criterion are derived in terms of linear matrix inequalities. Simulation results show the effectiveness of the proposed criterion.