Finite-time synchronization of fractional-order chaotic systems via sliding mode control

This paper investigates the finite-time sliding mode control (SMC) problem for fractional-order chaotic systems (FCSs). Existing finite-time stability criteria for nonlinear systems are typically restricted to a parameter range of α∈(0,1), which limits their applicability in controller design. To overcome this limitation, a novel finite-time stability theorem is established for general nonlinear systems, extending the parameter domain to α∈(0,+∞). Based on this theorem, a finite-time stability criterion for FCSs is derived under a double-integrating sliding mode controller. The proposed framework is then applied to the design of finite-time robust SMC for FCSs and to the fractional-order Lorenz system. Moreover, numerical simulations on two fractional-order chaotic systems quantitatively confirm that, with a suitable choice of α, the convergence rate can be expedited by 50%, accompanied by a marked improvement in transient performance, thereby validating the effectiveness of the proposed control scheme.