Global Practical Conformable Stabilization by Output Feedback for a Class of Nonlinear Fractional-Order Systems

Researchers have explored the concept of "practical stability" in the literature, pointing out that stability investigations always guarantee "practical stability" and the inverse is not true. The concept "practical stability" means that the origin is not an equilibrium point and the convergence of the system state is towards a ball centered at the origin. The primary purpose of this work is to investigate the notation of practical stability for a new class of fractional-order systems using the general conformable derivative. As a second objective, the nonlinear condition chosen is novel in that it is not Lipschitz as is customary, which is original in and of itself. In addition, some new analysis related to the LMI techniques was used to prove the main results. To begin, a method of stabilization is provided. Following that, the proposed system's observer design is presented. Also, the principle of separation is described. Finally, a numerical example is offered to demonstrate the proposed methodology's validity.