Stability analysis of interconnected complex nonlinear systems using the Lyapunov and Finsler property

This study focuses on the question of the stability analysis of complex interconnected nonlinear systems using the property of Lyapunov and Finsler. The main idea is to minimize the effect of interconnections between the subsystems, for that, we use the Lyapunov function and the H∞ control, then app...

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Bibliographic Details
Published inMultimedia tools and applications Vol. 80; no. 13; pp. 19971 - 19988
Main Authors Zouhri, Amal, Boumhidi, Ismail
Format Journal Article
LanguageEnglish
Published New York Springer US 01.05.2021
Springer Nature B.V
Subjects
Computer Communication Networks
Computer Science
Control stability
Data Structures and Information Theory
Decentralized control
Decomposition
H-infinity control
Inequality
Liapunov functions
Linear matrix inequalities
Mathematical analysis
Multimedia
Multimedia Information Systems
Nonlinear systems
Special Purpose and Application-Based Systems
Stability analysis
Subsystems
Decentralized state feedback
H∞ control
Finsler
Linear matrix inequality (LMI)
Interconnected system
Lyapunov
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Summary:This study focuses on the question of the stability analysis of complex interconnected nonlinear systems using the property of Lyapunov and Finsler. The main idea is to minimize the effect of interconnections between the subsystems, for that, we use the Lyapunov function and the H∞ control, then applying Finsler’s lemma to release the conditions of stability, the independent matrices allow to obtain less conservative results. The proposed control approach is formulated in a minimization problem and derived in terms of linear matrix inequalities (LMIs) whose resolution yields the decentralized control gain matrices. All the developed results are tested on two representative examples and compared with some recent previous ones .
ISSN:1380-7501
1573-7721
DOI:10.1007/s11042-020-10449-9