A New Approach on the Modelling and Analysis Stability of a Class of Fractional-Order Quasi-Polynomial Systems

Abstract

Stabilization and observation for nonlinear fractional derivative systems remain open problems in automatic due to the fractional nature and nonlinearity of these systems. The present paper studies global stability by the return output for fractional systems. First, we give some definitions of fractional calculus and the quasi-polynomial (QP) and Lotka-Volterra (LV) systems. Then, we analyze their stabilities as well as linear (LMI) and bilinear (BMI) matrix inequalities. In order to solve the controller design problem. The goal of this paper is to investigate the global and local stability of a dynamic fractional order system using the quasi-polynomial and LV representation. Then, we use the LMI to study the stabilization of this fractional system.