Disturbance and uncertainty rejection performance for fractional-order complex dynamical networks

This paper investigates the synchronization issue for a family of time-delayed fractional-order complex dynamical networks (FCDNs) with time delay, unknown bounded uncertainty and disturbance. A novel fractional uncertainty and disturbance estimator (FUDE) based feedback control strategy is proposed to not only synchronize the considered FCDNs but also guaranteeing the precise rejection of unmodelled system uncertainty and external disturbance. Especially, in FUDE-based approach, model uncertainties and external disturbance are integrated as a lumped disturbance and it does not require a completely known system model or a disturbance model. On the other hand, the design algorithm for the proposed control strategy is based on the state-space framework, rather than frequency-based design methodologies in the literature, which helps for predominant comprehension of the inner system behaviour. Also, by the temperance of Lyapunov stability theory and fractional calculus, a set of adequate conditions in the linear matrix inequality framework is obtained, which guarantees the robust synchronization of the closed-loop system. Furthermore, an iterative optimization algorithm is proposed to improve control robustness against the external disturbance and model uncertainties. Finally, two numerical illustrations including financial network model, where the influence of adjustment of macro-economic policies in the entire financial system are given to exhibit the rightness and important features of the acquired theoretical results.