Positivity and Stability Analysis for Fractional-Order Delayed Systems: A T-S Fuzzy Model Approach

Abstract

This article investigates positivity, external positivity, and asymptotic stability for a large class of incommensurate fractional-order nonlinear systems (FONSs) with bounded multiple time-varying delays by virtue of the T-S fuzzy method. The Laplace transformation technique is used to obtain the solutions of T-S fuzzy FONSs. A sufficient and necessary condition is derived for characterizing (internal) positivity, and certain criteria are also provided to guarantee external positivity of FONSs with or without time-varying delays. It is indicated that the positivity of the considered systems is determined purely by system matrices rather than the magnitudes of time-varying delays. Moreover, a sufficient and necessary condition for asymptotic stability of positive FONSs is obtained, and a state-feedback controller is also designed to guarantee that state variables not only converge to the origin asymptotically but also remain nonnegative, where the control gain matrix is obtained by solving an linear programming (LP) problem. Three numerical simulation examples are given to expound validity and feasibility of the theoretical results.