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Convergence properties of the Riccati difference equation in optimal filtering on nonstabilizable systems. (English) Zbl 0536.93057

The paper discusses solutions of the algebraic Riccati equation and the Riccati difference equation with regard to existence, uniqueness, and some other properties. It is assumed that the system is observable or detectable but not necessarily stabilizable. Particular interest is given to systems with uncontrollable roots on the unit circle, i.e. systems which have purely deterministic disturbances including sine waves and drift terms. The new results detailed here clarify some misconceptions in the literature concerning the conditions for asymptotic time invariance of Kalman filters, which may have had their application unnecessarily restricted in the past.
Reviewer: H.D.Fischer

MSC:

93E11 Filtering in stochastic control theory
39A11 Stability of difference equations (MSC2000)
93D20 Asymptotic stability in control theory
62M20 Inference from stochastic processes and prediction
30C15 Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral)
93B55 Pole and zero placement problems
93C40 Adaptive control/observation systems
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