Probability-one homotopy algorithms for full and reduced order H 2/H∞ controller synthesis

Homotopy algorithms for both full- and reduced-order LQG controller design problems with an H^∞ constraint on disturbance attenuation are developed. The H^∞ constraint is enforced by replacing the covariance Lyapunov equation by a Riccati equation whose solution gives an upper bound on H² performance. The numerical algorithm, based on homotopy theory, solves the necessary conditions for a minimum of the upper bound on H² performance. The algorithms are based on a minimal parameter formulation: Ly-Bryson-Cannon´s 2×2 block parametrization. Numerical experiments suggest that the combination of a globally convergent homotopy method and a minimal parameter formulation applied to the upper bound minimization gives excellent results for mixed-norm H ²/H^∞ synthesis. The nonmonotonicity of homotopy zero curves is demonstrated, proving that algorithms more sophisticated than standard continuation are necessary