Mohammad Ghamgosar - Academic Center for Education, Cultural and Research (ACCECR) Rasht, Iran
Seyed Mehdi Mirhosseini-Alizamini - Department Mathematics, Payam Noor University(PNU)Tehran, Iran

In this article, a strategy based on fractional order integral sliding mode control will be presented, based on which a class of delayed fractional order non-linear systems including disturbance and uncertainty can be stabilized. To achieve this goal, we provide a fractional integral sliding surface and by choosing a discrete control law, we guarantee that the state variables will remain on it after reaching the sliding surface. To prove this issue, we state and prove a theorem. In the following, using Razumukhin's stability theorem for delayed systems and linear matrix inequality, we state a theorem for calculating the effective parameter in calculating the sliding surface. A numerical example is simulated to show the effectiveness of the results. Finally, we end this article with a conclusion..

Delay systems, Fractional order systems, Sliding mode control, Linear matrix inequality