Estimating the Region of Attraction on Controlled Complex Networks With Time-Varying Delay

The importance of estimating the region of attraction (ROA) on complex networks has drawn attention very recently. However, challenging problems arise when applying the existing theory to networks with delay. In this article, we estimate the ROA on controlled complex networks with time-varying delay. A delay-independent ROA estimation method is derived at first. This method can deal with general delay and is convenient to use due to its independence of the delay. Accordingly, it may cause conservativeness. To further reduce the conservativeness, delay-dependent ROA estimation is established for networks with small delay by developing a new technique of dealing with the delay. Numerical simulations are provided to verify the theoretical results.