Regular Papers

International Journal of Control, Automation and Systems 2016; 14(6): 1464-1474

Published online October 25, 2016

https://doi.org/10.1007/s12555-015-0141-9

© The International Journal of Control, Automation, and Systems

Robust Sliding Mode-H∞ Control Approach for a Class of Nonlinear Systems Affected by Unmatched Uncertainties using a Poly-quadratic Lyapunov Function

Wajdi Saad*, Anis Sellami, and Germain Garcia

TUNIS University

Abstract

This paper proposes a robust sliding mode-H∞ control design methodology for a class of nonlinear systems with unmatched parametric uncertainty and external disturbance. The design procedure combines the high robustness of the sliding mode control (SMC) with the H∞ norm performance. First, based on linear matrix inequalities (LMI) technique and multiple Lyapunov functions approach, the sliding surface design problem is formulated as a H∞ state-feedback control for a reduced uncertain nonlinear system with polytopic representation. Then, a sliding mode controller that drives the system states to the sliding surface in finite time and maintains a sliding mode is constructed. Finally, a comparative study is done to prove the effectiveness of the results."

Keywords H∞ control, poly-quadratic Lyapunov function, sliding mode control, unmatched uncertainties.

Article

Regular Papers

International Journal of Control, Automation and Systems 2016; 14(6): 1464-1474

Published online December 1, 2016 https://doi.org/10.1007/s12555-015-0141-9

Copyright © The International Journal of Control, Automation, and Systems.

Robust Sliding Mode-H∞ Control Approach for a Class of Nonlinear Systems Affected by Unmatched Uncertainties using a Poly-quadratic Lyapunov Function

Wajdi Saad*, Anis Sellami, and Germain Garcia

TUNIS University

Abstract

This paper proposes a robust sliding mode-H∞ control design methodology for a class of nonlinear systems with unmatched parametric uncertainty and external disturbance. The design procedure combines the high robustness of the sliding mode control (SMC) with the H∞ norm performance. First, based on linear matrix inequalities (LMI) technique and multiple Lyapunov functions approach, the sliding surface design problem is formulated as a H∞ state-feedback control for a reduced uncertain nonlinear system with polytopic representation. Then, a sliding mode controller that drives the system states to the sliding surface in finite time and maintains a sliding mode is constructed. Finally, a comparative study is done to prove the effectiveness of the results."

Keywords: H&infin, control, poly-quadratic Lyapunov function, sliding mode control, unmatched uncertainties.

IJCAS
February 2025

Vol. 23, No. 2, pp. 359~682

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