Order-Dependent Stability and Stabilization Conditions for Fractional-Order Systems With Distributed Delays

This brief aims to analyze the stability and stabilization conditions for fractional-order systems with distributed delays (FOSDDs). Firstly, an order-dependent stability condition for nominal FOSDDs is obtained through utilizing the small gain theorem. Secondly, an robust stability condition for FOSDDs with norm-bounded uncertainties is derived using the proposed order-dependent stability condition. Furthermore, the state feedback controllers are designed to robustly stabilize FOSDDs with norm-bounded uncertainties. The achieved results are presented utilizing linear matrix inequalities (LMIs). Lastly, two numerical instances are presented to demonstrate the effectiveness of acquired conditions.