This article is concerned with the problem of finite-time mixed outer synchronization (FMOS) of complex networks with coupling time-varying delay. FMOS is a recently developed generalized synchronization concept, i.e., in which different state variables of the corresponding nodes can evolve into finite-time complete synchronization, finite-time anti-synchronization, and even amplitude finite-time death simultaneously for an appropriate choice of the controller gain matrix. Some novel stability criteria for the synchronization between drive and response complex networks with coupling time-varying delay are derived using the Lyapunov stability theory and linear matrix inequalities. And a simple linear state feedback synchronization controller is designed as a result. Numerical simulations for two coupled networks of modified Chua's circuits are then provided to demonstrate the effectiveness and feasibility of the proposed complex networks control and synchronization schemes and then compared with the proposed results and the previous schemes for accuracy.

The fault detection (FD) problem for systems with both model uncertainty and external disturbance is investigated in this article. First, the mathematical models of systems with model uncertainty and disturbance, systems with additive faults, and systems with multiplicative faults are established with both left and right coprime factorization. Then, an observer-based FD scheme is proposed and the FD thresholds are derived for both open-loop and closed-loop manners. The necessary conditions on multiplicative FD are obtained and the fault detectability analyses are carried out with the aid of the gap metric technique. Finally, the effectiveness of the proposed method is illustrated by a case study on a cart dynamic system.