Delay-dependent criteria for robust stability and stabilization of fractional-order time-varying delay systems

Abstract

In this paper, the robust stability and stabilization problems for fractional-order time-varying delay systems are investigated. Firstly, a new fractional-order Razumikhin theorem is given. By using the proposed fractional-order Razumikhin theorem, novel delay-dependent stability conditions for both nominal and uncertain linear fractional-order time-varying delay systems are derived. The results are in form of linear matrix inequalities, which are convenient for application and calculation. Then, the obtained stability conditions are utilized to derive a state feedback stabilization controller. To tackle the computational difficulty of the controller design method, a local optimization algorithm is proposed. Finally, three examples are provided to illustrate that the proposed results are valid and less conservative.