Averaging results pertaining to the implementation of hybrid feedback via PWM control

Abstract

Stability and robustness analysis for a class of hybrid dynamical systems via the averaging method is presented. Using the notions of strong and weak average, the time-varying hybrid system is approximated by a time-invariant hybrid system. We show that the solutions of the actual time-varying hybrid system and its weak or strong average can be made arbitrarily close on compact time domains under the assumption of forward completeness for the average systems and for appropriate sets of disturbances. The results include PWM hybrid feedback control system as a special case. In addition, it is also shown that input-to-state stability (ISS) of the strong (weak) average implies appropriate ISS properties for the actual system and asymptotic stability of the average system implies semi-global practical asymptotic stability of the actual system in the case of no disturbances. Through a PWM power converter example, we show that the main results can be used as a framework for a systematic design of hybrid controllers for electronic power systems.