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IMA Journal of Mathematical Control and Information 1987 4(1):93-107; doi:10.1093/imamci/4.1.93
© 1987 by Institute of Mathematics and its Applications
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Quadratic-Mean Convergence and Mean-Square Stability for Discrete Linear Systems: A Hilbert-Space Approach

C. S. KUBRUSLY

Department of Research and Development, National Laboratory for Scientific Computation—LNCC/CNPq R. Lauro Müller 455, Rio de Janeiro, RJ, 22290, Brazil
Department of Electrical Engineering, Catholic University—PUC/RJ, R. Marques de S. Vicente 209 Rio de Janeiro, RJ, 22453, Brazil

Let H be a separable Hilbert space and let H be the Hilbert space of all second order H-valued random variables. This paper deals with limiting properties for random sequences in H. Quadratic-mean convergence is investigated under the assumption of asymptotic weak uncorrelatedness. This leads to degenerate quadratic-mean limits. The mean-square stability problem for infinite-dimensional discrete linear systems driven by asymptotically uncorrelated input disturbances is analysed in detail. It is shown how mean-square stability acts on the quadratic-mean convergence of the state sequence.


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