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LMI-Observer-Based Stabilizer for Chaotic Systems in the Existence of a Nonlinear Function and Perturbation

Authors :
Farhad Bayat
Arthur Chang
Hamede Karami
Saleh Mobayen
Marzieh Lashkari
Source :
Mathematics, Volume 9, Issue 10, Mathematics, Vol 9, Iss 1128, p 1128 (2021)
Publication Year :
2021
Publisher :
MDPI AG, 2021.

Abstract

In this study, the observer-based state feedback stabilizer design for a class of chaotic systems in the existence of external perturbations and Lipchitz nonlinearities is presented. This manuscript aims to design a state feedback controller based on a state observer by the linear matrix inequality method. The conditions of linear matrix inequality guarantee the asymptotical stability of the system based on the Lyapunov theorem. The stabilizer and observer parameters are obtained using linear matrix inequalities, which make the state errors converge to the origin. The effects of the nonlinear Lipschitz perturbation and external disturbances on the system stability are then reduced. Moreover, the stabilizer and observer design techniques are investigated for the nonlinear systems with an output nonlinear function. The main advantages of the suggested approach are the convergence of estimation errors to zero, the Lyapunov stability of the closed-loop system and the elimination of the effects of perturbation and nonlinearities. Furthermore, numerical examples are used to illustrate the accuracy and reliability of the proposed approaches.

Details

ISSN :
22277390
Volume :
9
Database :
OpenAIRE
Journal :
Mathematics
Accession number :
edsair.doi.dedup.....8168051153b932eb9c47e201173ffc78
Full Text :
https://doi.org/10.3390/math9101128