New criteria for synchronization stability of continuous complex dynamical networks with non-delayed and delayed coupling

The synchronization stability problem of general complex dynamical networks with non-delayed and delayed coupling is investigated based on a piecewise analysis method, the variation interval of the time delay is firstly divided into several subintervals, by checking the variation of derivative of a Lyapunov functional in every subinterval, several new delay-dependent synchronization stability conditions are derived in the form of linear matrix inequalities, which are easy to be verified by the LMI toolbox. Some numerical examples show that, when the number of the divided subintervals increases, the corresponding criteria can provide much less conservative results.