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LQG control with an $H\sb{\infty}$ performance bound: A Riccati equation approach. (English) Zbl 0674.93069
Summary: An LQG control-design problem involving a constraint on $H\sb{\infty}$- disturbance attenuation is considered. The $H\sb{\infty}$ 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 $L\sb 2$ performance. In contrast to the pair of separated Riccati equations of standard LQG theory, the $H\sb{\infty}$- constrained gains are given by a coupled system of three modified Riccati equations. The coupling illustrates the breakdown of the separation principle for the $H\sb{\infty}$-constrained problem. Both full- and reduced-order design problems are considered with an $H\sb{\infty}$ attenuation constraint involving both state and control variables. An algorithm is developed for the full-order design problem and illustrative numerical results are given.

##### MSC:
 93E20 Optimal stochastic control (systems) 93B50 Synthesis problems 46J15 Banach algebras of differentiable or analytic functions, $H^p$-spaces 15A24 Matrix equations and identities
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