A class of relaxation algorithms for finding the periodic steady-state solution in nonlinear systems

An improvement in the author's previous algorithm for computing periodic steady-state solutions in nonautonomous systems is proposed that enables efficient computation of the solutions in autonomous systems. In addition, the derivations more clearly demonstrate the impact that the s- to z-plane mapping has on the equation formulation, specifically in the computation of the “A” and “B” matrices. A class of relaxation algorithms is proposed for the efficient solution of both nonautonomous and autonomous systems. Finally, simulation results on a van der Pol oscillator are presented that demonstrate the potential of the proposed algorithms. In addition, these simulations show how the use of different mappings from the s- to z-plane effect the solution estimates, and how the use of different mappings may be exploited to improve the efficiency of finding solutions