Exponential synchronisation of hybrid impulsive and switching dynamical networks with time delays

This study formulates and studies a model of hybrid impulsive and switching dynamical networks with time delays. There are two separable switching functions acting on the network. One drives inherent network structures and the other induces finite-state feedback in the control law. These hybrid networks have both continuous-time and discrete-time dynamics. At each moment, the coupling structure changes from one graph to another. At the same time, the continuous state variables may jump from one value to another. Time delays considered in this paper exist in isolated dynamical nodes, interconnections and impulsive noise disturbances. Based on Lyapunov stability theory, some new sufficient criteria are derived for exponential convergence of disagreement dynamics, which implies that network synchronisation of such hybrid-delayed network is achieved. An illustrative example of a delayed chaotic network with switching topology and impulse effects is used to demonstrate the main results.