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Reduced-order filtering with energy-to-peak performance for discrete-time Markovian jumping systems. (English) Zbl 1067.93058

The objective of this paper is to study discrete-time Markov jump linear systems. The design of a reduced-order (energy-to-peak) \(l_2\)-\(l_\infty\) filter is presented. The filter can make an error gain which satisfies a prescribed \(l_2\)-\(l_\infty\) norm bound constraint.
Sufficient conditions for the existence of the \(l_2\)-\(l_\infty\) filter are proposed in terms of LMIs with a coupling rank constraint set. A numerical example is added to illustrate the procedures.

MSC:

93E11 Filtering in stochastic control theory
60J75 Jump processes (MSC2010)
93C55 Discrete-time control/observation systems
93B11 System structure simplification
15A39 Linear inequalities of matrices
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