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Minimum System Sensitivity Study of Linear Discrete Time Systems for Fault Detection
Joint Authors
Source
Mathematical Problems in Engineering
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-13, 13 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-03-04
Country of Publication
Egypt
No. of Pages
13
Main Subjects
Abstract EN
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 ℋ− index, which measures the worst fault sensitivity.
This paper is concerned with characterizing ℋ− index for linear discrete time systems.
First, a necessary and sufficient condition on the lower bound of 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 ℋ− index.
In addition, for linear time-invariant systems in infinite time horizon, based on the definition of the 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 ℋ− index is not completely dual to ℋ∞ norm.
Finally, several numerical examples are given to illustrate the main results.
American Psychological Association (APA)
Li, Xiaobo& Liu, Hugh H. T.. 2013. Minimum System Sensitivity Study of Linear Discrete Time Systems for Fault Detection. Mathematical Problems in Engineering،Vol. 2013, no. 2013, pp.1-13.
https://search.emarefa.net/detail/BIM-1008903
Modern Language Association (MLA)
Li, Xiaobo& Liu, Hugh H. T.. Minimum System Sensitivity Study of Linear Discrete Time Systems for Fault Detection. Mathematical Problems in Engineering No. 2013 (2013), pp.1-13.
https://search.emarefa.net/detail/BIM-1008903
American Medical Association (AMA)
Li, Xiaobo& Liu, Hugh H. T.. Minimum System Sensitivity Study of Linear Discrete Time Systems for Fault Detection. Mathematical Problems in Engineering. 2013. Vol. 2013, no. 2013, pp.1-13.
https://search.emarefa.net/detail/BIM-1008903
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1008903