Impulsive observer-based stabilisation of uncertain linear systems

This study considers impulsive observer-based control of uncertain linear systems. A novel time-varying Lyapunov function is introduced to explore the hybrid characteristic of the impulsive observed-based control systems. By applying the time-varying Lyapunov function method combined with convex combination technique, sufficient conditions for the existence of the impulsive observer-based controller is derived in terms of linear matrix inequalities (LMIs). The control and observer gains can be obtained from the feasible solutions of the newly-obtained LMI-based conditions. Two numerical examples are presented to show the efficiency of the proposed design method.