On solving discrete-time periodic Riccati equations

Author:	Varga Andras, German Aerospace Center, DLR - Oberpfaffenhofen, Germany
Topic:	2.2 Linear Control Systems
Session:	Analysis and Synthesis of Linear Control Systems II
Keywords:	periodic systems, Riccati equation, deadbeat control, numerical methods

Abstract

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.