ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

Vol. LXXIV, 1 (2005)
p. 107 - 126

The quadratic control for linear discrete-time systems with independent random
perturbations in Hilbert spaces connected with uniform observability

V. M. Ungureanu


Abstract.  The optimal control problem for linear discrete-time, time-varying systems with state dependent noise and quadratic control is considered. The asymptotic behavior of the solution of the related discrete-time Riccati equation is investigated. The existence of an optimal control, under stabilizability and uniform observability (respectively detectability) conditions, for the given quadratic cost function is proved.

Keywords: Quadratic control, Riccati equation, uniform observability.  

AMS Subject classification:  93E20, 49N10, 39A11.

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