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 period ic steady-state solutions in nonautonomous systems is proposed that en ables efficient computation of the solutions in autonomous systems. In addition, the derivations more clearly demonstrate the impact that th e s- to z-plane mapping has on the equation formulation, specifically in the computation of the ''A'' and ''B'' matrices. A class of relaxat ion algorithms is proposed for the efficient solution of both nonauton omous and autonomous systems. Finally, simulation results on a van der Pol oscillator are presented that demonstrate the potential of the pr oposed algorithms. In addition, these simulations show how the use of different mappings from the s- to z-plane effect the solution estimate s, and how the use of different mappings may be exploited to improve t he efficiency of finding solutions.