Design of a Fixed-Time Stabilizer for Uncertain Chaotic Systems Subject to External Disturbances

Amir Rezaie, Saleh Mobayen (), Mohammad Reza Ghaemi, Afef Fekih and Anton Zhilenkov
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Amir Rezaie: Department of Mathematics, Faculty of Sciences, University of Zanjan, Zanjan 45371-38791, Iran
Saleh Mobayen: Department of Electrical Engineering, Faculty of Engineering, University of Zanjan, Zanjan 45371-38791, Iran
Mohammad Reza Ghaemi: Department of Mathematics, Faculty of Sciences, University of Zanjan, Zanjan 45371-38791, Iran
Afef Fekih: Department of Electrical and Computer Engineering, University of Louisiana at Lafayette, Lafayette, LA 70504, USA
Anton Zhilenkov: Department of Cyber-Physical Systems, St. Petersburg State Marine Technical University, 190121 Saint-Petersburg, Russia

Mathematics, 2023, vol. 11, issue 15, 1-14

Abstract: This paper addresses the fixed-time stability problem of chaotic systems with internal uncertainties and external disturbances. To this end, new sliding-mode surfaces are introduced to design fixed-time controllers for the stabilization of perturbed chaotic systems. First, the required conditions for deriving fixed-time stability are determined. Then, using the obtained stability theorems and sliding mode techniques, the controllers are synthesized. The proposed controller enables the convergence of the trajectories of the chaotic system to the origin in finite time, independently of the initial conditions. The performance of the proposed approach is assessed using a simulation study of a PMSM system and the Matouk system. Among the advantages of the proposed controller are its robustness to external disturbances and the boundedness of the settling time to a constant value for any initial condition.

Keywords: chaotic systems; Lyapunov function; fixed-time stability; robust control; sliding mode control (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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