Mixed Reduced-Order Filtering for Discrete-Time Markov Jump Linear Systems With Partial Information on the Jump Parameter

This article deals with the H_{2} , H_{\infty} , and mixed H_{2} / H_{\infty} reduced-order filters for discrete-time Markov jump linear systems, within the context of partial observation of the jump parameter. It is considered that the Markov chain parameter, denoted by \theta(k) , is not obse...

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Bibliographic Details
Published in:IEEE transactions on systems, man, and cybernetics. Systems man, and cybernetics. Systems, 2023-10, Vol.53 (10), p.1-0
Main Authors: de Oliveira, Andre M., dos Santos, Sergio R. Barros, Costa, Oswaldo L. V.
Format: Article
Language:English
Subjects:
Context
Control systems
Filter design (mathematics)
filtering
H-infinity optimization
Hidden Markov models
hidden Markov models (HMM)
jump parameter systems
Linear matrix inequalities
Linear systems
Markov chains
Markov processes
Mathematical analysis
Minimization
Network control
Parameters
Performance analysis
Real-time systems
Reduced order filters
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Summary:This article deals with the H_{2} , H_{\infty} , and mixed H_{2} / H_{\infty} reduced-order filters for discrete-time Markov jump linear systems, within the context of partial observation of the jump parameter. It is considered that the Markov chain parameter, denoted by \theta(k) , is not observable but, instead, only an estimation, represented by \hat \theta(k) , is available for the filter design. Sufficient synthesis conditions for the filter design, based on linear matrix inequalities, are provided. These conditions for the H_{2} and H_{\infty} filters are not conservative in the sense that, for the full-order case and perfect information of the Markov parameter, they become also necessary. Simplified conditions are derived for the Bernoulli case. This article is concluded with an illustrative example in the context of networked control systems, in which we study the effects of reducing the order of the filter on the estimation performance.
ISSN:2168-2216
2168-2232
DOI:10.1109/TSMC.2023.3283210