Mixed \(H_2 / H_{\infty}\) fault detection filter for Markovian jump linear systems
type: Item
instance of: scholarly article
title: Mixed \(H_2 / H_{\infty}\) fault detection filter for Markovian jump linear systems
zbMATH Open document ID: 1427.93230
DOI: 10.1155/2018/4239696
author: Leonardo de Paula Carvalho
author: André Marcorin de Oliveira
author: Oswaldo Luiz do Valle Costa
published in: Mathematical Problems in Engineering
publication date: 2019-02-08T00:00:00Z
review text: Summary: We tackle the mixed \(H_2 / H_{\infty}\) fault detection filter problem for a Markov jump linear system (MJLS) in the discrete-time domain. We present three distinct formulations: the first one is to minimize an upper bound on the \(H_2\) subject to a given upper value on the \(H_{\infty}\) norm; the second one is the opposite situation; that is, we minimize an upper bound on \(H_{\infty}\), subject to a given restriction on the \(H_2\) norm; and the third one is the minimization of a weighted combination of the upper bound of both the \(H_2\) and \(H_{\infty}\) norms. We present new conditions in the form of linear matrices inequalities (LMI) that provide the design of the fault detection filter. We also present results for the so-called mode-independent case and the design of robust \(H_{\infty}\) filters in the sense that the system matrices are uncertain. In order to illustrate the feasibility of the proposed approaches, a numerical example is presented.
Mathematics Subject Classification ID: 93E10
Mathematics Subject Classification ID: 93B36
Mathematics Subject Classification ID: 93E11
Mathematics Subject Classification ID: 60J74
zbMATH DE Number: 7018943
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/4239696
OpenAlex ID: W2884517183
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description: scientific article; zbMATH DE number 7018943