H∞H∞ cluster synchronization and state estimation for complex dynamical networks with mixed time delays

The paper investigates H∞H∞ cluster synchronization and state estimation for complex dynamical networks with mixed time delays. A novel concept of H∞H∞ cluster synchronization is proposed to quantify against the exogenous disturbance of the complex networks. Based on the Lyapunov stability theory, H∞H∞ cluster synchronization criteria are derived in the form of linear matrix inequalities. The solvability of derived conditions depends not only on the attenuation level but also the initial values of complex networks. The H∞H∞ state estimation is studied for the same complex networks with the purpose of designing a state estimator to estimate the network states through available output measurements. Finally, two numerical examples are provided to demonstrate the effectiveness of the obtained theoretical results.