Novel Stability and Stabilization Conditions for Fractional‐Order Systems With Mixed Delays

ABSTRACT This paper investigates the stability and stabilization of the fractional‐order systems with mixed delays (FOSMDs), including discrete delays and distributed delays. At first, an order‐dependent stability condition for FOSMDs is derived with the use of small gain theorem. Then, based on the stability condition, a robust stability condition for the uncertain FOSMDs with polytopic uncertainties is proposed. Next, with the robust stability condition and the designed state feedback controllers, a robust stabilization condition for the uncertain FOSMDs is proposed. At last, several numerical examples are put forward to manifest the effectiveness of the obtained results.