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

Abstract

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.

Practical Stability for Conformable Time-Delay Systems

“…In recent years, fractional diferential equations (FDEs) have found applications in many problems in physical. As in most of the time, these equations cannot be solved exactly except when we know some particular solutions or else we refer to the study of existence and uniqueness of solutions using some fundamental theorems of functional analysis (the Banach contraction theorem) for the other FDEs (Riemann-Liouville and Caputo) (see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]).…”

“…Indeed, there are a few works on the study of the practical stability of conformable FDEs (see [9,11]). To the best of our knowledge, there is no existing work about the practical stability of conformable systems with delays, and motivated by the previous works in the literature, our article covers this gap by using the LMI method.…”