This paper deals with finite-time control problem for nonlinear fractional-order systems with order 0 < α <1. We first derive sufficient conditions for finite-time stabilization based on Caputo derivative calculus and Lyapunov-like function method. Then, by introducing a new type of the cost control function, we study guaranteed cost control problem for such systems. In terms of linear matrix inequalities, an explicit expression for state and output feedback controllers is given to make the closed-loop system finite-time stable and to guarantee an adequate cost level of the performance.

The proposed method is applied to analyze the finite-time control problem for a class of linear uncertain FOSs. Finally, numerical examples are given to illustrate the validity and effectiveness of the proposed results.