An approach to analyze the stability of a class of hybrid systems with delay

This paper proposes an approach to analyze the stability of a class of hybrid systems with delay, where there only exists a bounded delay in continuous evolution but discrete transition occurs instantly. First, the class of hybrid systems is modeled as a hybrid automaton with delay (HAD). Based on the HAD model, the sufficient conditions of the stability for an equilibrium are presented. Furthermore, for the case where the continuous subsystems of the hybrid system are all linear time invariant systems with time delay, the linear matrix inequality (LMI) technique is employed to analyze the stability. Finally, a numerical example is presented to illustrate the developed results.