Minimal-order observers for linear functions of a state vector

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Abstract
The synthesis of observers for linear functions of a state vector is considered. A systematic procedure is developed for generating and testing dynamical systems of increasing dimension until certain key observer equations, interpreted in a geometrical sense, are satisfied. This yields a characterization of the candidate observer of least possible order that satisfies all the requirements for an observer except, perhaps, stability. An extension of the basic procedure yields characterization of higher-order candidate observers. The minimal-order observer problem is solved by checking these candidate observers, in order of increasing dimension, for stabilizability or pole assignability using the free parameters in their characterizations. The techniques developed are illustrated by means of numerical examples.