Enhancing the Stability of the Switched Systems Using the Saltation Matrix

Abstract

Controlling switched systems is a difficult task, even when dealing with piecewise linear systems (CPWLs), which consist of a set of linear differential equations and a set of switching conditions. This difficulty is largely due to the loss of linearity in the entire system, and it is necessary to solve differential and algebraic equations to determine the solution. In this paper, a new method to tune the parameters of the controllers applied to switched systems is derived using information from the saltation matrix, particularly its induced norm. First, the parameters are tuned using classical methods, and then, after analyzing the norm of the saltation matrix, a new set of parameters that guarantees the stability of the period-1 orbit is obtained. The method is validated using analytical solutions for two different systems (boost and boost-flyback power converters) and is also experimentally validated for the boost-flyback power converter.