Practical Finite-Time Synchronization of Fractional-Order Complex Dynamical Networks With Application to Lorenz’s Circuit

This paper focuses on addressing the practical finite-time synchronization (PFTS) problem of heterogeneous fractional-order complex dynamical networks (FCDNs) through event-triggered feedback control (ETFC). Firstly, a novel practical finite-time stability lemma is proposed based on the fractional-order differential inequality <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$_{t_{0}}^{C}D_{t}^{\alpha } V\left ({{ t }}\right) \le - {p_{1}}V\left ({{ t }}\right) - {p_{2}}{V^{\beta } }\left ({{ t }}\right) + q$ </tex-math></inline-formula>, which plays a crucial role in analyzing PFTS. Secondly, a novel ETFC protocol is designed where the information transmission of the controller occurs at a sequence of state-dependent instants. Thirdly, using the aforementioned lemma and fractional Lyapunov theory, synchronization criteria for heterogeneous FCDNs can be derived, and Zeno behavior is excluded. Finally, the numerical example involving the PFTS of a fractional-order Lorenz’s circuit is provided to demonstrate the effectiveness of the proposed theoretical results.