On discrete-time H∞ control: a J-lossless coprime factorization approach

A relatively simple approach, based on chain scattering descriptions, to the synthesis of discrete-time controllers that result in a cost function with H^∞ norm strictly less than a prespecified bound is presented. The approach relies on a J -lossless numerator and a conjugate J-lossless denominator. The approach also gives a connection at the transfer function level between three algebraic Riccati equations that are associated with the solution of a discrete-time H^∞ control problem. The derivation is carried out in terms of transfer function matrices, although the final formulas are in state space