Synchronization for a class of discrete complex dynamical networks in presence of Markov jump topology and actuator saturation

This work addresses the synchronization problem for discrete complex dynamical networks (CDNs) that are associated with Markov jump outer coupling, parameter uncertainties, actuator saturation, and time delay. Especially, the uncertainties which occur in the inner coupling matrix are categorized with the use of the interval matrix approach. The main purpose of this work is to design an appropriate state feedback controller with a saturation effect that guarantees asymptotic synchronization and also satisfy a prescribed level of mixed H∞ and passivity performance for the addressed CDNs. Moreover, a new set of adequate criteria are expressed in the form of linear matrix inequalities to synchronize the considered network plant. The above synchronization criteria are retrieved with the support of an appropriate Lyapunov–Krasovskii functional, Kronecker product properties together with Jensen's inequality and Abel lemma. Eventually, the efficiency and superiority of our proposed synchronization criteria are demonstrated through two numerical examples.