Numerical solution of the general mixed H2/H∞ optimization problem

The necessary conditions for the nonconservative solution of the mixed H₂/H_∞ optimization problem have been presented. It was found that, for a controller of the same order as the plant, these conditions require a neutrally stablizing solution to a Riccati equation and a solution to a Lyapunov equation which has no unique solution. This paper develops a method for solving a suboptimal problem that converges to the true mixed solution while requiring only stabilizing solutions to Riccati equations and unique solutions to Lyapunov equations. Two numerical examples are presented. The numerical solution technique is based on the Davidon-Fletcher-Powell algorithm.