Mixed Linear Complementarity Problems for the Analysis of Limit Cycles in Piecewise Linear Systems

Piecewise linear systems can exhibit periodic steady state oscillations. An interesting case study is represented by limit cycles in Lur'e systems. In this paper mixed linear complementarity models are used to compute limit cycles in autonomous piecewise linear systems. It is shown how a complementarity representation of the feedback characteristic and the dynamics discretization allow to formulate a mixed linear complementarity problem whose solution provides an accurate prediction of the steady state oscillation. Numerical results show the effectiveness of the proposed technique for the computation of stable, unstable and sliding limit cycles.