A Chain Scattering-Matrix Description Approach to H^∞ Control

This note employs chain scattering-matrix descriptions and J-lossless coprime factorizations to develop a relatively simple method for the synthesis of the continuous-time H^∞ suboptimal control. Analogous to the Youla parameterization of all stabilizing controllers, we derive an identity to generate all suboptimal controllers. The derivation we give is carried out in terms of transfer function matrices although the final formulae are in state space. The approach provides a clear connection at the transfer function level between coprime factorizations and algebraic Riccati equations that are associated with the solutions of the problem.