Order-dependent LMI-based stability and stabilization conditions for fractional-order time-delay systems using small gain theorem

In this article, based on small gain theorem, the stability, and stabilization problems for fractional-order time-delay systems are investigated. First, one order-dependent and delay-independent stability condition, and two order-dependent and delay-dependent stability conditions of nominal fractional-order time-delay systems are derived by developing different feedback loop structures. Then, by employing the proposed order-dependent stability conditions, the robust stability conditions for fractional-order time-delay systems with norm-bounded uncertainties are given. Moreover, state feedback controllers that robustly stabilize fractional-order time-delay systems with norm-bounded uncertainties are obtained. The proposed results are in terms of linear matrix inequalities. With the help of LMI solvers, these criteria can be easily verified. Finally, numerical examples are provided to illustrate that the proposed criteria are valid and less conservative than the existing ones.