Interpolation approach to H ∞ estimation and its interconnection to loop transfer recovery

Abstract This paper proposes to solve the H ∞ optimal estimation problem via interpolation theory. The advantages of this approach are the following. (i) Direct and simple solutions can be obtained for the optimal estimators; (ii) frequency weightings on estimation error and disturbance can be easily incorporated; and (iii) unnecessary high observer gains can be avoided. We also show the interconnection between the H ∞ optimal estimation problem and the optimal loop transfer recovery problem. The interpolation approach applies to both continuous-time and discrete-time systems.

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