On solving discrete-time periodic Riccati equations

Kurzfassung

Two numerically reliable algorithms to compute the periodic nonnegative definite stabilizing solution ofdiscrete-time periodic Riccati equations are proposed. The first method represents an extension ofthe periodic QZ algorithm to non-square periodic pairs, while the second method represents an extension of a quotient-product swapping and collapsing "fast" algorithm. Both approaches are completely general being applicable to periodic Riccati equations with time varying dimensions as well as with singular control weighting. For the "fast" method, reliable software implementation is available in a recently developed Periodic Systems Toolbox.