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IMA Journal of Mathematical Control and Information Advance Access originally published online on March 2, 2009
IMA Journal of Mathematical Control and Information 2009 26(1):105-127; doi:10.1093/imamci/dnp001
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© The author 2009. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Optimal control for linear discrete-time systems with Markov perturbations in Hilbert spaces

Viorica Mariela Ungureanu{dagger}

"Constantin Brancusi" University of Tirgu-Jiu, Bulevardul Republicii nr.1, Tg-Jiu, Gorj, Romania

{dagger} Email: vio{at}utgjiu.ro

Received on September 12, 2007; Accepted on December 26, 2008

In this article, we discuss a quadratic control problem for linear discrete-time systems with Markov perturbations in Hilbert spaces, which is linked to a discrete-time Riccati equation defined on certain infinite-dimensional ordered Banach space. We prove that under stabilizability and stochastic uniform observability conditions, the Riccati equation has a unique, uniformly positive, bounded on N and stabilizing solution. Based on this result, we solve the proposed optimal control problem. An example illustrates the theory.

Keywords: discrete-time stochastic systems; stochastic observability; Riccati equation; optimal control.


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