Extended limiting forms of optimum observers and LQG regulators

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Abstract
The general problem of optimal estimation in singular observation systems is considered. By generalizing the limiting procedure of Friedland, explicit and closed expressions for the transfer matrices of the optimum observer as well as for the optimal control law in the singular measurement LQG problem are derived. The number of integrators that are required for the implementation of the singular optimum observer is shown, for square systems, to be equal to the number of the system's zeros. The closed form of the optimum observer given here is advantageous as compared with existing procedures. Structural properties of the singular observation problem are discussed, and the role of the zeros of the system in such problems is clarified. The dual results for the case of stochastic ‘cheap’ control are also given.

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