Liu, Huaping; Sun, Fuchun; Sun, Zengqi Reduced-order filtering with energy-to-peak performance for discrete-time Markovian jumping systems. (English) Zbl 1067.93058 IMA J. Math. Control Inf. 21, No. 2, 143-158 (2004). 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. Reviewer: Anna Jaskiewicz (Wrocław) Cited in 6 Documents 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 Keywords:linear matrix inequality (LMI); reduced-order filtering; energy-to-peak performance; discrete-time Markov jump linear systems PDFBibTeX XMLCite \textit{H. Liu} et al., IMA J. Math. Control Inf. 21, No. 2, 143--158 (2004; Zbl 1067.93058) Full Text: DOI