This paper deals with finite-time control problem for nonlinear fractional-order systems with order \(0<\alpha <1\). 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.

本文针对阶为\（0 <\ alpha <1 \）的非线性分数阶系统的有限时间控制问题。我们首先基于Caputo导数演算和Lyapunov-like函数方法导出有限时间稳定的充分条件。然后，通过介绍一种新型的成本控制功能，我们研究了此类系统的保证成本控制问题。根据线性矩阵不等式，给出了状态和输出反馈控制器的明确表达式，以使闭环系统有限时间稳定，并保证足够的性能成本水平。该方法被用于分析一类线性不确定FOS的有限时间控制问题。最后，通过数值算例说明了所提出结果的有效性和有效性。