H 2 optimal control for a wide class of discrete-time linear stochastic systems

In this article, the problem of H 2 -control of a discrete-time linear system subject to Markovian jumping and independent random perturbations is considered. Different H 2 performance criteria (often called H 2 -norms) are introduced and characterised via solutions of some suitable linear equations...

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Bibliographic Details
Published inInternational journal of systems science Vol. 40; no. 10; pp. 1029 - 1049
Main Authors Dragan, Vasile, Morozan, Toader
Format Journal Article
LanguageEnglish
Published Taylor & Francis Group 01.10.2009
Subjects
discrete-time linear systems
independent random perturbations
Markov chains
Markov processes
norms
optimal control
Primary: 93E20
robust control
Secondary: 93C55
stochastic systems
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ISSN0020-7721
1464-5319
DOI10.1080/00207720902974629

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Summary:In this article, the problem of H 2 -control of a discrete-time linear system subject to Markovian jumping and independent random perturbations is considered. Different H 2 performance criteria (often called H 2 -norms) are introduced and characterised via solutions of some suitable linear equations on certain spaces of symmetric matrices. Some aspects specific to the discrete-time framework are revealed. The problem of optimisation of H 2 -norms is solved under the assumption that full state vector is available for measurements. One shows that among all stabilising controllers of higher dimension, the best performance is achieved by a zero-order controller. The corresponding feedback gain of the optimal controller is constructed based on the stabilising solution of a system of discrete-time generalised Riccati equations.
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ISSN:0020-7721
1464-5319
DOI:10.1080/00207720902974629