Robust Stability and Stabilization of Incommensurate Fractional-Order Uncertain Systems: A Parameter Space Method

Abstract

This paper discusses the robust stability and stabilization of incommensurate fractional-order uncertain systems by the parameter space method. Analyzing the Jacobian matrix around the equilibrium points is a direct way to test whether systems satisfy the asymptotic stability theorem. The asymptotic stability theorem of incommensurate fractional-order systems is an expansion of the commensurate ones. This expansion often makes the characteristic equation of the Jacobian matrix high-dimensional. When systems are with uncertain parameters, it is difficult to solve all roots of the high-dimensional equation. In this paper, a parameter space method is proposed by transforming the high-dimensional characteristic equation into a parameter-dependent equation, for selecting the complete stable region from the parameter space directly. One example shows robust stability and stabilization results by using the parameter space method.