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This paper aims to design the full-order and reduced-order fault detection filters (FDFs) under unified linear matrix inequality (LMI) conditions for polytopic uncertain discrete-time singular Markovian jump systems (DTSMJSs) with time-varying delays. The highlight of this work lies in that the designed full-order and reduced-order FDFs are suitable for four different state transition probability matrices (TPMs), and the reduced-order fault detection filter (FDF) not only meets fault detection (FD) sensitivity conditions of the complex systems but also improve the efficiency of FD. With the help of the Lyapunov function theory and convex polyhedron technique, a sufficient condition is presented to ensure that the singular model error augmented system is stochastically admissible with a prescribed H∞ performance index. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed design method.

In this paper, the problem of finite-time adaptive synchronization is investigated for two different delayed neural networks with unknown parameters. Two adaptive control approaches are designed in order to synchronize the neural networks in finite time. The first controller fully involves the information of time-varying delay and the second one is delay-independent under the case that time-varying delay is unknown. By utilizing the Lyapunov stability theory, sufficient conditions are proposed to guarantee the finite-time synchronization of the addressed neural networks. In addition, the settling time for synchronization is estimated. Finally, two numerical simulations are used to illustrate the correctness and effectiveness of the proposed methods.