Global robust ℋ−/ℋ∞ synchronization for a class of dynamical networks

By proposing the framework of global robust ℋ_-/ℋ_∞ synchronization, this study focuses on the robust fault detection issue within the synchronization for a class of nonlinear dynamical networks composed by identical Lur´e systems. Under such synchronization scheme, the error dynamical system is globally asymptotically stable, the effect of external disturbances is suppressed, and at the same time, the network is sensitive to possible faults based on a mixed ℋ_-/ℋ_∞ performance. Sufficient conditions in terms of linear matrix inequalities (LMIs) are established. Furthermore, the fault sensitivity ℋ_- index can be optimized via a convex optimization algorithm. A network model composed of identical Chua´s circuits is adopted as a numerical example.