Numerical solvers for discrete-time periodic riccati equations

Abstract

This paper analyzes the performance of two different methods for solving discrete-time periodic Riccati equations. The first approach is based on the computation of the periodic Schur form of the monodromy matrices, the reordering of the eigenvalues in this form, and the solution of certain linear systems. The second approach performs a sequence of orthogonal swaps in the monodromy matrices, and then employs the so-called matrix disk function, to solve the equations. Numerical experiments arts reported for both methods on serial and shared memory platforms.