Time-stepping Methods for Computing Periodic Solutions in Maximally Monotone Set-valued Dynamical Systems

In this paper, we study a class of set-valued dynamical systems that satisfy maximal monotonicity properties. This class includes linear relay systems, linear complementarity systems, and linear mechanical systems with dry friction under some conditions. We discuss two numerical schemes based on time-stepping methods for the computation of the periodic solutions when these systems are periodically excited. We provide formal mathematical justifications for the numerical schemes in the sense of consistency, which means that the continuous-time interpolations of the numerical solutions converge to the continuous-time periodic solution when the discretization step vanishes. The two timestepping methods are applied for the computation of the periodic solution exhibited by a power electronic converter and the corresponding methods are compared in terms of approximation accuracy and computation time.