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The problem of performance deterioration in optimal regulators, which is caused by the introduction of observers, is investigated. Time-invariant Luenberger observers with minimal order are used as state estimators for deterministic linear time-invariant systems. A necessary and sufficient condition for the performance deterioration to be made arbitrarily small is given, under the assumption that the observer state can be chosen in terms of the regulator output at initial time.It is shown, according to this condition, that n-m=1, where n denotes the dimension of the regulator state and m denotes the dimension of the measurable output vector, implies the existence of observers with minimal order satisfying a prescribed small deterioration of the performance, and n-m≥2 implies, in almost all cases, that if the initial state, x(0), of the regulator belongs to a fixed subspace, V, of Rn, the performance deterioration, ΔJ, is bounded away from zero as shown by the form ΔJ≥ρ||x||2, where ρ is a positive constant independent of the choice for observers.
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