Lyapunov uniform stability and stabilization of fractional order positive time delay systems

This paper is concerned with Lyapunov uniform stability and stabilization of fractional order positive time delay systems. A copositive Lyapunov-Krasovskii functional is first constructed for fractional order positive time delay systems. By means of the newly present functional, a sufficient condition for the Lyapunov uniform stability of fractional order positive time delay systems is established in terms of linear programming. Then, the Lyapunov uniform stabilization of the underlying systems is solved, where a state-feedback control law is designed. Finally, two illustrative examples are given to show the correctness of the present results.