Observer-Based Quasi-Projective Functional Synchronization of Parameters Mismatch Dynamical Networks With Mixed Time-Varying Delays Under Impulsive Controllers

This article is primarily concerned with the quasi-projective synchronization phenomenon between the a leader node and response nodes of an observer-based delayed dynamical network (DDN) instead of complete synchronization because of projective functional factor and parameters mismatch. First, a novel observer-based drive-response dynamical network (DN) with time-varying discrete-distributed delays and parameters mismatch is constructed to study its synchronization phenomena by introducing projective functional factor. Then, in order to obtain the sufficient criteria of quasi-projective synchronization for this system, the special impulsive control strategies and the definition of matrix measure are introduced in this article. After that, by the different impulsive phenomena and the properties of the projective functional factor, appropriate Lyapunov functional, Cauchy matrix, and inequality techniques are used to discuss and derive quasi-projective synchronization conditions of this observer-based delayed DN. In addition, some conclusions of synchronization for special DNs models are given as corollaries. Finally, an example with one leader node and four different response nodes and its corresponding simulation figures are given to demonstrate the obtained results.