Synchronization and state estimation for singular complex dynamical networks with time-varying delays

The paper investigates the synchronization and state estimation for singular complex dynamical networks with time-varying delays. Firstly, a modified Lyapunov–Krasovskii functional is constructed by employing the more general decomposition approach, the novel delay-dependent synchronization conditions are derived in terms of linear matrix inequalities, which can be easily solved by various convex optimization algorithms. Secondly, the state estimation problem is then studied for the same complex networks, where the purpose is to design a state estimator to estimate the network states through available output measurement, a delay-dependent asymptotically stability condition is established for the system of the estimation error. Some numerical examples are exploited to illustrate the effectiveness of the proposed synchronization and state estimation conditions.