Computation of limit cycles and forced oscillations in discrete-time piecewise linear feedback systems through a complementarity approach

Limit cycles and forced oscillations in piecewise liner (PWL) feedback systems are difficult to be computed without a priori knowledge of the structure of the periodic solution. Even in that case the explicit computation of the solution is possible only assuming simple models. In this paper, by representing discrete-time PWL feedback systems as linear complementarity systems, we show that periodic oscillations can be computed by solving suitable static linear complementarity problems. An efficient algorithm for computing such solutions is adopted. Limit cycles in autonomous relay feedback systems and forced oscillations in pulse width modulated DC/DC power converters are easily found by solving the proposed complementarity problem, provided that the discretized complementarity system well approximates the original continuous-time system.