Stability and stabilization of positive fractional linear systems by state-feedbacks

Abstract

Notations of the practical stability and of the asymptotic stability of positive and cone fractional 1D and 2D linear systems are introduced. Necessary and sufficient conditions for the practical stability and the asymptotic stability of positive and cone fractional 1D and 2D linear systems are established. It is shown that the checking of the practical stability and asymptotic stability of positive 2D linear systems can be reduced to testing the stability of corresponding 1D positive linear systems. Three LMI approaches are proposed for checking the stability of positive fractional linear systems. LMI approach is applied to compute gain matrices of state-feedbacks such that closed-loop systems are positive and asymptotically stable. The proposed methods are illustrated on numerical examples.