Sampled data $H_{\infty}$ synchronization of time-varying delay complex networks with randomly occurring controller gain fluctuations

In this paper, we research the problem of $H_{\infty}$ synchronization of sampled data for time-varying delay complex networks with randomly occurring controller gain fluctuations. Firstly, a sampled data controller with non-fragile memory is designed, which involves signaling delays. The controller gain fluctuations are in a randomized manner and obey a certain Bernoulli distributed white noise sequence. Secondly, a suitable Lyapunov-Krasovskii function is constructed and derived by methods such as FMB inequality and Schur's complementary lemma to obtain a sufficient condition for the synchronization of complex dynamic network systems. The linear matrix inequality method is then used to find the maximum allowable sampling period. Finally, a numerical example is used to verify the feasibility and effectiveness of the proposed method in this paper.