Stability and Stabilization of Fractional Order Time Delay Systems

Mihailo Lazarević

In this paper, some basic results of the stability criteria of fractional order system with time delay as well as free delay are presented. Also, we obtained and presented sufficient conditions for finite time stability and stabilization for (non)linear (non)homogeneous as well as perturbed fractional order time delay systems. Several stability criteria for this class of fractional order systems are proposed using a recently suggested generalized Gronwall inequality as well as “classical” Bellman-Gronwall inequality. Some conclusions for stability are similar to those of classical integerorder
differential equations. Finally, a numerical example is given to illustrate the validity of the proposed procedure.

 

Key words: nonlinear system, system stability, system stabilization, system with delay, time delay, perturbation, fractional order system.