Computation of limit cycles in Lur’e systems

Computation of limit cycles in autonomous piecewise linear feedback systems in Lur’e form is considered. It is shown how the complementarity representation of the feedback characteristic allows to represent the discretized closed loop system as a linear complementarity system. A static linear complementarity problem, whose solutions correspond to periodic solutions of the discrete–time system, is formulated. The proposed technique is able to compute steady state oscillations with known period for continuous–time systems, so as demonstrated by simulation results on the Chua electrical circuit and on other Lur’e systems which exhibit asymmetric unstable and sliding limit cycles.