Minimum system sensitivity study of linear discrete time systems for fault detection
type: Item
instance of: scholarly article
title: Minimum system sensitivity study of linear discrete time systems for fault detection
zbMATH Open document ID: 1296.93052
DOI: 10.1155/2013/276987
author: Hugh H. T. Liu
author: Xiaobo Li
published in: Mathematical Problems in Engineering
publication date: 2014-10-13T00:00:00Z
review text: Summary: Fault detection is a critical step in the fault diagnosis of modern complex systems. An important notion in fault detection is the smallest gain of system sensitivity, denoted as \(\mathcal H_-\) index, which measures the worst fault sensitivity. This paper is concerned with characterizing \(\mathcal H_-\) index for linear discrete time systems. First, a necessary and sufficient condition on the lower bound of \(\mathcal H_-\) index in finite time horizon for linear discrete time-varying systems is developed. It is characterized in terms of the existence of solution to a backward difference Riccati equation with an inequality constraint. The result is further extended to systems with unknown initial condition based on a modified \(\mathcal H_-\) index. In addition, for linear time-invariant systems in infinite time horizon, based on the definition of the \(\mathcal H_-\) index in frequency domain, a condition in terms of algebraic Riccati equation is developed. In comparison with the well-known bounded real lemma, it is found that \(\mathcal H_-\) index is not completely dual to \(\mathcal H_\infty\) norm. Finally, several numerical examples are given to illustrate the main results.
Mathematics Subject Classification ID: 93B36
Mathematics Subject Classification ID: 93C55
Mathematics Subject Classification ID: 93E12
zbMATH DE Number: 6354600
Wikidata QID: Q59025513
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/276987
OpenAlex ID: W2025002988
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description: scientific article; zbMATH DE number 6354600