LQG control with an H∞ performance bound: a riccati equation approach

An LQG control-design problem involving a constraint on H_∞ disturbance attenuation is considered. The H_∞ performance constraint is embedded within the optimization process by replacing the covariance Lyapunov equation by a Riccati equation whose solution leads to an upper bound on L₂ performance. In contrast to the pair of separated Riccati equations of standard LQG theory, the H_∞-constrained gains are given by a coupled system of three modified Riccati equations. The coupling illustrates the breakdown of the separation principle for the H_∞-constrained problem. Both full- and reduced-order design problems are considered with an H_∞ attenuation constraint involving both state and control variables. An algorithm is developed for the full-order design problem and illustrative numerical results are given. A more complete version of this paper is given in [41].