Analysis of periodic solutions in piecewise linear feedback systems via a complementarity approach

Periodic solutions in piecewise linear feedback systems in Luré form, composed by a linear time invariant dynamical system closed in feedback through a static piecewise linear mapping are analyzed. A procedure for representing the closed loop system in complementarity form, based on resistors-diode-sources equivalent circuits of the piecewise linear characteristic is presented. Conditions for the existence of discrete–time periodic solutions in terms of solvability of a suitable static linear complementarity problem are obtained. Numerical results for a chaotic circuit show that the proposed approach can be also used to predict periodic solutions of continuous–time systems in Luré form provided that consistency of the discretization is assumed.