Hinfinity multivariable-control-law synthesis

The linear-quadratic-Gaussian (LQG) embedding approach for solving the H_infinity control problem is much simplified by the introduction of a special Youla parameterisation and auxiliary LQG problem. The approach has the advantage over previous solutions that most of the analysis concerns an auxiliary LQG problem. The influence of the weighting function which changes the controller from a usual LQG design to an H_infinity -norm minimisation device is transparent in this new problem formalism. The cost functions minimised in both H₂ and H_infinity problems include cross-product terms for greater generality. The conditions under which a simplified design procedure may be used are established and related to the solution of a 1-block Nehari problem.