LQG control with an H/sup infinity / performance bound: a Riccati equation approach

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Abstract
An LQG (linear quadratic Gaussian) control-design problem involving a constraint on H/sup infinity / disturbance attenuation is considered. The H/sup infinity / 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 L/sub 2/ performance. In contrast to the pair of separated Riccati equations of standard LQG theory, the H/sup infinity /-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/sup infinity /-constrained problem. Both full- and reduced-order design problems are considered with an H/sup infinity / attenuation constraint involving both state and control variables. An algorithm is developed for the full-order design problem and illustrative numerical results are given.<>