Common Lyapunov Function Based on Kullback–Leibler Divergence for a Switched Nonlinear System
Joint Authors
Yoshinaga, Tetsuya
Fujimoto, Ken'ichi
Abou Al-Ola, Omar M.
Source
Mathematical Problems in Engineering
Issue
Vol. 2011, Issue 2011 (31 Dec. 2011), pp.1-12, 12 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2011-05-10
Country of Publication
Egypt
No. of Pages
12
Main Subjects
Abstract EN
Many problems with control theory have led to investigations into switched systems.
One of the most urgent problems related to the analysis of the dynamics of switched systems is the stability problem.
The stability of a switched system can be ensured by a common Lyapunov function for all switching modes under an arbitrary switching law.
Finding a common Lyapunov function is still an interesting and challenging problem.
The purpose of the present paper is to prove the stability of equilibrium in a certain class of nonlinear switched systems by introducing a common Lyapunov function; the Lyapunov function is based on generalized Kullback–Leibler divergence or Csiszár's I-divergence between the state and equilibrium.
The switched system is useful for finding positive solutions to linear algebraic equations, which minimize the I-divergence measure under arbitrary switching.
One application of the stability of a given switched system is in developing a new approach to reconstructing tomographic images, but nonetheless, the presented results can be used in numerous other areas.
American Psychological Association (APA)
Abou Al-Ola, Omar M.& Fujimoto, Ken'ichi& Yoshinaga, Tetsuya. 2011. Common Lyapunov Function Based on Kullback–Leibler Divergence for a Switched Nonlinear System. Mathematical Problems in Engineering،Vol. 2011, no. 2011, pp.1-12.
https://search.emarefa.net/detail/BIM-493443
Modern Language Association (MLA)
Abou Al-Ola, Omar M.…[et al.]. Common Lyapunov Function Based on Kullback–Leibler Divergence for a Switched Nonlinear System. Mathematical Problems in Engineering No. 2011 (2011), pp.1-12.
https://search.emarefa.net/detail/BIM-493443
American Medical Association (AMA)
Abou Al-Ola, Omar M.& Fujimoto, Ken'ichi& Yoshinaga, Tetsuya. Common Lyapunov Function Based on Kullback–Leibler Divergence for a Switched Nonlinear System. Mathematical Problems in Engineering. 2011. Vol. 2011, no. 2011, pp.1-12.
https://search.emarefa.net/detail/BIM-493443
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-493443