Analysis and synthesis of linear hybrid systems with state-triggered jumps

This paper investigates first the stability and L 2 -gain problems for a class of linear hybrid control systems with state-triggered jumps by using an extended Lyapunov-like function (ELF) technique. The obtained results are then applied to facilitate the joint design of a hybrid controller (linear controller plus reset law) for a continuous-time linear time-invariant (LTI) plant. The hybrid H ∞ synthesis conditions are expressed in linear matrix inequalities (LMIs) with two line search parameters. An inverted pendulum example is used to illustrate the effectiveness of the proposed approach.