ROBUST STABILIZATION OF CONFORMABLE FRACTIONAL-ORDER ONE-SIDED LIPSCHITZ NONLINEAR SYSTEMS VIA OBSERVER-BASED CONTROL

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.