A non‐recursive method for solving the general discrete‐time riccati equations related to the H_∞ control problem

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.