Synchronization of uncertain hybrid switching and impulsive complex networks

Abstract

• Hybrid switches and impulses are characterized by dwell-time constraint. • Dwell-time partitioning and convex combination techniques are used. • Results unify synchronizing and desynchronizing impulses. • Unsynchronized networks can be synchronized by desynchronizing impulses. This paper considers the asymptotic synchronization problem for a class of uncertain complex networks (CNs) with hybrid switching and impulsive effects. The switches and impulses occur by following a time sequence which is characterized by dwell-time constraint. By designing Lyapunov function with time-varying matrix parameter, two general synchronization criteria formulated by matrix inequalities are first given, which unify synchronizing and desynchronizing impulses. Then specific conditions in terms of linear matrix inequalities (LMIs) are given by partitioning the dwell time and using convex combination technique. Compared with those criteria which are only applicable to pure synchronizing impulses or pure desynchronizing impulses, our results are more practical. It is shown that the switched impulsive CNs (SICNs) can be synchronized by desynchronizing impulses even though CNs without impulse are unsynchronized. Numerical examples are given to show the effectiveness of our new results.