Limit cycles in switching capacitor systems: A Lur´e approach

This paper deals with the stability of limit cycles for a class of linear switching systems. Such applications arise in the context of electrical networks. An autonomous RLC circuit with switching capacitor is considered. A two-step method is given to design limit cycles for this application. First we give a procedure for determining the feasible approximate frequencies at which limit cycles may exist. Then, we give a method to design nonlinear controllers to achieve a stable limit cycles at a given frequency. An example is given to illustrate the methods.