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Morais, Cecília F.; Braga, Márcio F.; Lacerda, Márcio J.; Oliveira, Ricardo C. L. F.; Peres, Pedro L. D.

\(\mathcal{H}_2\) and \(\mathcal{H}_\infty\) filter design for polytopic continuous-time Markov jump linear systems with uncertain transition rates. (English) Zbl 1330.93229

Int. J. Adapt. Control Signal Process. 29, No. 10, 1207-1223 (2015).
Summary: This paper addresses the problems of \(\mathcal{H}_2\) and \(\mathcal{H}_\infty\) full-order filter design for continuous-time Markov jump linear systems subject to uncertainties. Different from the available methods in the literature, the main novelty of the proposed approach is the possibility of computing bounds to the \(\mathcal{H}_2\) and \(\mathcal{H}_\infty\) norms of the augmented system composed by the uncertain Markov jump linear system plus the robust filter through Lyapunov matrices depending polynomially on the uncertainties affecting independently the matrices of each operation mode and the transition rate matrix. By means of a suitable representation of the uncertainties, the proposed filter design conditions are expressed in terms of linear matrix inequality relaxations associated with searches on scalar parameters. As an additional flexibility, the conditions can be used to synthesize filters with partial, complete, or null Markov mode availability. Numerical experiments illustrate that the proposed approach is more general and can be less conservative than the available methods.

Cited in 9 Documents

MSC:

93E11 Filtering in stochastic control theory
93E10 Estimation and detection in stochastic control theory
60J75 Jump processes (MSC2010)
93B36 \(H^\infty\)-control

Keywords:

Markov jump linear systems; uncertain transition rates; polytopic uncertainties; \(\mathcal{H}_2\) and \(\mathcal{H}_\infty\) filtering; linear matrix inequalities

Software:

SeDuMi; YALMIP
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Full Text: DOI

References:

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