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- Title
Robust H<sub>2</sub> filtering of phase‐type semi‐Markov jump linear systems with cluster observations.
- Authors
de Oliveira, André M.; Costa, Oswaldo L. V.
- Abstract
In this work we study the design of H2$$ {H}_2 $$ filters for phase‐type (PH) semi‐Markov jump linear systems, considering partial information on the system's operating mode and possible parameter uncertainties. With respect to the mode of operation, it is assumed that the state space of the semi‐Markov chain can be written as the union of disjoint sets, called clusters, and the only information available to the filter is which cluster the state of the semi‐Markov chain belongs to. A new linear matrix inequality (LMI) parameterization employing the slack variable technique is introduced for the design of switching full‐order filters according to the cluster observations so that suitable bounds on the H2$$ {H}_2 $$ norm of the estimation error are guaranteed for the uncertain system. If the system is restricted to be a Markov jump linear system and the Markov chain is assumed to be perfectly measured, the design conditions are shown to be also necessary leading to the optimal full‐order filter. Furthermore, the general filter can be particularized into an observer form for the case in which the system matrices are the same within each cluster and there are no parameter uncertainties except for possible uncertainties affecting the transition rates of the jumping process. The paper concludes with an illustrative example in the context of networked control systems.
- Subjects
LINEAR systems; LINEAR matrix inequalities; MARKOVIAN jump linear systems; KALMAN filtering; UNCERTAIN systems; FILTERS &; filtration; MARKOV processes; INFORMATION storage &; retrieval systems
- Publication
International Journal of Robust & Nonlinear Control, 2024, Vol 34, Issue 8, p5126
- ISSN
1049-8923
- Publication type
Article
- DOI
10.1002/rnc.7253