H-INFINITY 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 appro ach has the advantage over previous solutions that most of the analysi s concerns an auxiliary LQG problem. The influence of the weighting fu nction which changes the controller from a usual LQG design to an H(in finity)-norm minimisation device is transparent in this new problem fo rmalism. The cost functions minimised in both H-2 and H(infinity) prob lems include cross-product terms for greater generality. The condition s under which a simplified design procedure may be used are establishe d and related to the solution of a 1-block Nehari problem.