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Steady-state Kalman filtering with an $H\sb{\infty}$ error bound. (English) Zbl 0684.93081
Summary: An estimator design problem is considered which involves both $L\sb 2$ (least squares) and $H\sb{\infty}$ (worst-case frequency-domain) aspects. Specifically, the goal of the problem is to minimize an $L\sb 2$ state- estimation error criterion subject to a prespecified $H\sb{\infty}$ constraint on the state-estimation error. The $H\sb{\infty}$ estimation- error 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 the $L\sb 2$ state-estimation error. The principal result is a sufficient condition for characterizing fixed- order (i.e., full- and reduced-order) estimators with bounded $L\sb 2$ and $H\sb{\infty}$ estimation error. The sufficient condition involves a system of modified Riccati equations coupled by an oblique projection, i.e., idempotent matrix. When the $H\sb{\infty}$ constraint is absent, the sufficient condition specializes to the $L\sb 2$ state-estimation result given by the first author and {\it D. C. Hyland} [IEEE Trans. Autom. Control AC-30, 583-585 (1985; Zbl 0555.93056)].

##### MSC:
 93E11 Filtering in stochastic control 46J15 Banach algebras of differentiable or analytic functions, $H^p$-spaces 15A24 Matrix equations and identities
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##### References:
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