STATE-SPACE APPROACH TO DISCRETE-TIME H-INFINITY CONTROL

State-space solutions to a discrete-time H infinity problem are given. For a given number gamma > 0 we give a characterization of all controllers such that the H infinity norm of the closed-loop transfer function is less than gamma. The approach taken is based on the solution of two Riccati equations using the stable deflating subspace of a symplectic pencil. This ensures that no unneccessary assumptions on the 'A' matrix on the realization of the transfer function are needed. While the results are the direct analogues of those in the continuous time, the state-space derivation is considerably more difficult.