AN OPTIMIZED GLOBAL SYNCHRONIZATION ON SDDCN

The complex networks have been gaining increasing research attention because of their potential applications in many real-worldsystems from a variety of fields such as biology, social systems, linguistic networks, and technological systems. In this paper, the problem ofstochastic synchronization analysis is investigated for a new array of coupled discrete time stochastic complex networks with randomly occurrednonlinearities (RONs) and time delays. The discrete-time complex networks under consideration are subject to: 1) stochastic nonlinearities thatoccur according to the Bernoulli distributed white noise sequences; 2) stochastic disturbances that enter the coupling term, the delayed couplingterm as well as the overall network; and 3) time delays that include both the discrete and distributed ones. Note that the newly introduced RONsand the multiple stochastic disturbances can better reflect the dynamical behaviors of coupled complex networks whose information transmissionprocess is affected by a noisy environment. By constructing a novel Lyapunov-like matrix functional, the idea of delay fractioning is applied todeal with the addressed synchronization analysis problem. By employing a combination of the linear matrix inequality (LMI) techniques, thefree-weighting matrix method and stochastic analysis theories, several delay-dependent sufficient conditions are obtained which ensure theasymptotic synchronization in the mean square sense for the discrete-time stochastic complex networks with time delays. The criteria derived arecharacterized in terms of LMIs whose solution can be solved by utilizing the standard numerical software. While these solvers are significantlyfaster than classical convex optimization algorithms, it should be kept in mind that the complexity of LMI computations remains higher than thatof solving, say, a Riccati equation. For instance, problems with a thousand design variables typically take over an hour on today’s workstations. However, this thesis proposes LMI optimization technique to solve this problem. The advantage of the proposed approach is that resultingstability criterion can be used efficiently via existing numerical convex optimization algorithms such as the interior-point algorithms for solvingLMIs