State estimation for linear impulsive systems

In this paper, we treat the fundamental problem of state estimation for a class of linear impulsive systems with time-driven impulsive effects. We show that a strong observability property enables an impulsive observer to be constructed that yields uniformly exponentially stable estimation error dynamics. This approach accommodates impulsive systems with arbitrarily-spaced impulse times and singular state transition matrices in a manner reminiscent of well-known results for time-varying discrete-time linear systems. As an example, an observer is constructed for an impulsive system that produces general cubic spline signals.