Impulsive observer and impulsive control for time-delay systems

In this paper, we study the problems of impulsive observer-based impulsive control for linear time-invariant systems with time-varying delays. Compared with traditional observer-based control schemes, our observer and controller are modelled by impulsive differential equations, where both the states of observer and controller are updated abruptly at impulse times and moreover, the information of time-varying delays is not required in both of observer and controller. By Lyapunov function method and impulsive delay differential inequality, some sufficient conditions for globally exponential stability of the closed-loop system are derived in terms of linear matrix inequalities (LMIs). Moreover, the gain matrices could be designed by solving the corresponding LMIs. Finally, a numerical example is pretended to illustrate the effectiveness of the proposed approach.