Input to state set stability for pulse width modulated control systems with disturbances

New results on set stability and input-to-state stability in pulse-width modulated (PWM) control systems with disturbances are presented. The results are based on a recent generalization of two time scale stability theory to differential equations with disturbances. In particular, averaging theory for systems with disturbances is used to establish the results. The nonsmooth nature of PWM systems is accommodated by working with upper semicontinuous set-valued maps, locally Lipschitz inflations of these maps, and locally Lipschitz parameterizations of locally Lipschitz set-valued maps.