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

Hamede Karami, Saleh Mobayen, Marzieh Lashkari, Farhad Bayat and Arthur Chang
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Hamede Karami: Department of Electrical Engineering, University of Zanjan, Zanjan 45371-38791, Iran
Saleh Mobayen: Department of Electrical Engineering, University of Zanjan, Zanjan 45371-38791, Iran
Marzieh Lashkari: Department of Electrical Engineering, University of Zanjan, Zanjan 45371-38791, Iran
Farhad Bayat: Department of Electrical Engineering, University of Zanjan, Zanjan 45371-38791, Iran
Arthur Chang: Bachelor Program in Interdisciplinary Studies, National Yunlin University of Science and Technology, Yunlin 64002, Taiwan

Mathematics, 2021, vol. 9, issue 10, 1-15

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.

Keywords: chaos control; output feedback; stabilization; Lipchitz system; observer-based control (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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