LMI-Based Control Design and Stability Analysis with a Conformable Fractional Derivative (CFD) for a Nonlinear Inverted Pendulum
DOI:
https://doi.org/10.36602/Keywords:
Inverted pendulum, conformable fractional derivative, LMIAbstract
This paper uses a conformable fractional derivative (CFD) to analyze stability and design controls for nonlinear systems, specifically the inverted pendulum. The system is described as a linear component and a nonlinear component that satisfies a Lipschitz condition, and a nonlinear state-space model is generated. An adequate stability condition is obtained using a quadratic Lyapunov function, which is then converted into a linear matrix inequality (LMI) via the Schur complement, with an additional term that accounts for the worst-case effect of nonlinearities. A feedback gain that ensures stability is obtained by resolving this inequality. The Lipschitz constant determines the controller's aggressiveness. The performance of the controller is shown when the integer order mathematical model is replaced with fractional order one.
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Copyright (c) 2026 Ali Omar M Alsharif، Ausama H. Ahmed، Abdolkarem S. Ebshish، Ahmed. M. A Zargoun، Omer Naifar، Asaad Jmal، Jihed HMAD (Author)
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