H ∞ Robust LMI-Based Nonlinear State Feedback Controller of Uncertain Nonlinear Systems with External Disturbances

Masoud Chatavi, Mai The Vu, Saleh Mobayen () and Afef Fekih
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Masoud Chatavi: Department of Mechanical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran 15875, Iran
Mai The Vu: School of Intelligent Mechatronics Engineering, Sejong University, Seoul 05006, Korea
Saleh Mobayen: Future Technology Research Center, National Yunlin University of Science and Technology, Douliou, Yunlin 64002, Taiwan
Afef Fekih: Department of Electrical and Computer Engineering, University of Louisiana at Lafayette, Lafayette, LA 70504, USA

Mathematics, 2022, vol. 10, issue 19, 1-19

Abstract: In this paper, we propose a nonlinear state feedback controller based on linear matrix inequality (LMI) for a class of nonlinear systems with parametric uncertainties and external disturbances. The primary goals of the proposed controller are to guarantee system stability and performance in the presence of system uncertainties and time-dependent disturbances. To meet the specified objectives, the LMI form is calculated as a hierarchical control structure. Using the Lyapunov stability function, the asymptotic stability of the nominal system obtained from the nonlinear state feedback is proven, and the LMI condition is attained. After applying the nonlinear state feedback controller, asymptotic stability conditions for the nominal system are constructed using the Lyapunov function, and the nonlinear state-feedback control mechanism is determined accordingly. Considering the external disturbance as input, the terms of the state matrices are substituted in the obtained LMI, and the LMI condition for a nominal system is achieved in the presence of disturbances. The asymptotic stability condition of the uncertain system in the presence of external disturbances is determined by adding uncertainties to the system. The proposed approach yields a simple control mechanism representing an independent of system order. The performance of the proposed approach was assessed using a simulation study of a ball and beam system.

Keywords: state feedback stability; linear matrix inequality; parametric uncertainty; external disturbance; robust control (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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