Delay-dependent and order-dependent stability and stabilization analysis of variable fractional order uncertain differential systems with time-varying delay via linear matrix inequality approach

Abstract

This paper concentrates on the robust stability and stabilization analysis of variable fractional order uncertain differential systems with time-varying delay. Firstly, by using a suitable Lyapunov–Krasovskii function and constructing an appropriate variable fractional order inequality, a novel delay-dependent and order-dependent stability theorem of the nominal systems is proposed. Then, based on the above stability conditions, the robust delay-dependent and order-dependent stability conditions for the uncertain systems are discussed. Moreover, in order to stabilize the nominal and uncertain systems, state feedback controllers are also derived with the help of the presented stability criteria. All the results are in the form of linear matrix inequalities. Finally, two numerical examples are provided to verify the effectiveness of the introduced theoretical formulation.