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Stability of multidimensional nonnegative systems

Authors
  • Ooba, Tatsushi1
  • 1 Nagoya Institute of Technology, Department of Mechanical Engineering, Gokiso-cho, Showaku, Nagoya, 466-8555, Japan , Nagoya
Type
Published Article
Journal
Circuits, Systems and Signal Processing
Publisher
Birkhäuser-Verlag
Publication Date
May 01, 2000
Volume
19
Issue
3
Pages
197–204
Identifiers
DOI: 10.1007/BF01204574
Source
Springer Nature
Keywords
License
Yellow

Abstract

The stability of discrete-time linear multidimensional dynamics is studied from the viewpoint of quadratic Lyapunov stability. The concept of a localized Lyapunov function is introduced to analyze the state behavior of multidimensional dynamics. It is shown that if the sum of the absolute-valued coefficient matrices of a multidimensional dynamics is stable in the sense that the spectral radius is less than unity, then any state transition of the multidimensional dynamics shows a step-by-step decrease with respect to an appropriately constructed localized diagonal Lyapunov function. The obtained result is a natural extension of an already-known result on the stability of nonnegative matrices.

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