Non-recursive method for solving the general discrete-time Riccati equations related to the H∞ control problem

Abstract

In this paper we propose a nonrecursive method for solving the general discrete-time algebraic Riccati equation related to the H∞ control problem (H∞-DARE). We have achieved this by casting the problem of solving a given H∞DARE to the problem of solving an auxiliary continuous-time algebraic Riccati equation associated with the H∞ control problem (H∞-CARE) for which the well known nonrecursive methods of solving are available. The advantages of our approach are: it reduces the computation involved in the recursive algorithms while giving much more accurate solutions, and it readily provides the properties of the general H∞-DARE.