ROBUST STABILIZATION OF CONFORMABLE FRACTIONAL-ORDER ONE-SIDED LIPSCHITZ NONLINEAR SYSTEMS VIA OBSERVER-BASED CONTROL
DOI:
https://doi.org/10.51453/2354-1431/2024/1245Keywords:
Conformable fractional-order systems; One-sided Lipschitz nonlinearity; Observer-based control; Lyapunov functional method; Linear matrix inequalityAbstract
This paper addresses the problem of robust stabilization for conformable fractionalorder nonlinear systems with one-sided Lipschitz conditions using observer-based control. Conformable fractional calculus is appropriate for a variety of real-world applications since it provides a more adaptable mathematical framework for explaining the dynamics of systems that display both integer and fractional-order behaviors. The key feature of this work is the use of the one-sided Lipschitz property, which relaxes the global Lipschitz condition, allowing for more general nonlinearities. By constructing an appropriate state observer, we estimate unmeasured states and develop a control law that guarantees asymptotic stabilization. Sufficient conditions for the existence of the observer and the controller are derived based on linear matrix inequalities. A numerical example is provided to demonstrate the effectiveness and robustness of the proposed method.
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