Hybrid synthesis for almost asymptotic regulation of linear impulsive systems with average dwell time

This paper deals with the hybrid output regulation problem for a class of linear impulsive systems with average dwell time. The hybrid regulator is constructed as a linear impulsive system that undergoes synchronous impulses with the controlled plant, and the hybrid synthesis conditions are formulated in terms of two matrix equations plus a set of linear matrix inequalities (LMIs). With the proposed hybrid synthesis scheme, both continuous-time and discrete-time dynamics of the hybrid regulator can be jointly synthesized by solving a convex optimization problem of minimizing the weighted ℒ₂ gain from the perturbation signal to the error output. A numerical example is used to demonstrate the proposed approach.