Hybrid adaptive and impulsive synchronisation of uncertain complex dynamical networks by the generalised Barbalat´s lemma

Robust local and global hybrid adaptive and impulsive synchronisation for a class of uncertain complex dynamical networks are investigated in this study, respectively. For the complex dynamical network with unknown but bounded non-linear couplings, with unknown bounds, hybrid adaptive and impulsive controllers are designed based on adaptive control theory and impulsive control theory. By the generalised Barbalat´s lemma, the uncertain complex dynamical network is proved to be locally or globally asymptotically synchronised. Several robust local and global hybrid adaptive and impulsive synchronisation criteria are also established. Two numerical examples are given to demonstrate the effectiveness of the proposed controller design methods.