Computation of limit cycles in Lur´e systems

Computation of limit cycles in autonomous piece wise 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.