Fractional comparison method and asymptotic stability results for multivariable fractional order systems

Abstract

This paper investigates the asymptotic stability of equilibrium points of multivariable fractional order systems where its state equations contain different fractional orders which lie between 0 and 1. First, a fractional comparison principle is presented. Then, some elementary comparison results for linear fractional order systems of different fractional orders are developed. Based on continuously differentiable quadratic function and comparison results, new sufficient conditions are established for the asymptotic stability of linear and nonlinear multivariable fractional order systems. Finally, a few illustrative examples are presented.