On the Existence and Construction of Common Lyapunov Functions for Switched Discrete Systems
- Authors: Kosov A.A.1, Kozlov M.V.2
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Affiliations:
- Matrosov Institute for System Dynamics and Control Theory
- National Research Mordovian State University
- Issue: Vol 12, No 4 (2018)
- Pages: 668-677
- Section: Article
- URL: https://journals.rcsi.science/1990-4789/article/view/213117
- DOI: https://doi.org/10.1134/S1990478918040075
- ID: 213117
Cite item
Abstract
Under consideration is the problem of stability of switched discrete systems with the generalized homogeneous right-hand sides. The conditions are obtained for the existence of the common Lyapunov function, and a method for its construction is proposed in the form of a combination of the partial Lyapunov functions obtained for isolated subsystems. For a special case of linear three-dimensional systems, some algorithms are proposed for constructing common Lyapunov functions as quadratic and fourth degree forms. Some examples illustrate the effectiveness of the proposed approach.
About the authors
A. A. Kosov
Matrosov Institute for System Dynamics and Control Theory
Author for correspondence.
Email: kosov_idstu@mail.ru
Russian Federation, ul. Lermontova 134, Irkutsk, 664033
M. V. Kozlov
National Research Mordovian State University
Email: kosov_idstu@mail.ru
Russian Federation, ul. Bol’shevistskaya 68, Saransk, 430005