Output feedback stabilization for linear impulsive systems

Abstract

In this paper, we address an output feedback stabilization problem for a class of linear impulsive systems that accommodate arbitrarily-spaced impulse times and possibly singular state transition matrices. By combining recent results for state feedback stabilization and state estimation, we show that a separation property holds and formulate an output feedback compensation scheme in which the feedback loop is closed between a discrete-time measurement and a continuous-time control input. Rather than directly adopting an observer-based structure involving the time-varying gains associated with the separate stabilization and estimation problems, we construct a purely discrete-time compensator followed by a memoryless generalized hold device that achieves closed-loop exponential stability.