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The issue of synchronizing delayed and complicated dynamical networks (CDNs) using sampling data is examined in this research. First, modified free-matrix-based integral inequalities (MFMBIIs), respectively, are generated from the current free-matrix-based integral inequalities (FMBIIs) [36] and [37] to optimize CDNs’ sampled-data synchronizing control’s efficiency. Following that, the intended data sampling controller is put forth to asymptotically and exponentially synchronize the CDNs by deploying the time-associated Lyapunov functional technique and convexity-based combining approach, which fully utilize the acceptable information with respect to the actual sampling interval. Finally, computational instances verify the validity of the present outcomes and especially show that a larger upper bound of the sampling interval can be obtained from our results.