Discrete-time H∞ control: the one-block case

A new solution for the discrete-time H_∞ optimal control problem is given. By using the Rosenbrock system matrix representation, it is shown that the assumption of not having poles at the origin, which is required in previous derivations, is not necessary. The generator of all solutions has a simple and direct expression in terms of the data of the problem. The parametrization provides further insight into the one-block problem by linking the authors´ pure algebraic approach with the one-step operator theoretic procedure. It is also shown that a particular solution, usually called the central one, always has a state space representation (i.e., it has no polynomial part)