Estimation of the Domain of Attraction on Controlled Complex Networks with Unbounded Time-varying Delay

This paper deals with the problem of the domain of attraction (DOA) estimation for complex networks with unbounded delay. Firstly, from the perspective of $\gamma -$stability, a time-varying differential inequality with unbounded time-varying is established, and various stabilities including polynomial stability and logarithmic stability are discussed. By removing restrictive monotonicity conditions, a novel inequality is developed. Subsequently, based on the proposed differential inequalities and the Lyapunov function approach, the local synchronization of complex network system with unbounded delay has been analyzed and some criteria for the DOA estimation are derived. Finally, two numerical examples are presented to verify the feasibility of theoretical findings.