RELATIONSHIP BETWEEN 3 DISCRETE-TIME H-INFINITY ALGEBRAIC RICCATI EQUATION SOLUTIONS

This paper presents a proof of a connection between the strong solutions to three algebraic Riccati equations which are associated with the solution of a discrete-time Hoo-optimal control problem. Of these solutions, denoted X"" Y 00 and Zoo, two parametrize a generator of all v-suboptirnal output-feedback controllers and one is associated with a dual state-feedback problem. The relationship is proved by establishing the existence of a similarity transformation between two symplectic matrix pencils which are associated with two of the Riccati equations. A similar result is known to exist in the continuous-time setting. © 1990 Taylor and Francis Group, LLC.