PROBABILITY-ONE HOMOTOPY ALGORITHMS FOR FULL-ORDER AND REDUCED-ORDER H-2 H-INFINITY CONTROLLER SYNTHESIS/

Homotopy algorithms for both full- and reduced-order LQG controller de sign problems with an H-infinity constraint on disturbance attenuation are developed. The H-infinity constraint is enforced by replacing the covariance Lyapunov equation by a Riccati equation whose solution giv es an upper bound on H-2 performance. The numerical algorithm, based o n homotopy theory, selves the necessary conditions for a minimum of th e upper bound on H-2 performance. The algorithms are based on two mini mal parameter formulations: Ly, Bryson and Cannon's 2x2 block parametr ization and the input normal Riccati form parametrization. An overpara metrization formulation is also proposed. Numerical experiments sugges t 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-infinity synthesis. The n onmonotonicity of homotopy zero curves is demonstrated, proving that a lgorithms more sophisticated than standard continuation are necessary.