This paper studies the stabilizability and instabilizability problems for delayed complex-valued memristive neural networks within finite-time intervals. First, more general assumptions for complex-valued activation functions are given. To check that whether the closed-loop system is stable within a finite-time interval, a novel nonlinear delayed controller with separable real-imaginary parts is designed. It includes two independent parameters different from the existing ones, which makes the controller more general but also leads to great difficulties. To overcome these difficulties, two new inequalities are proposed and proved. Then, through Lyapunov function approach, sufficient conditions are derived for the finite-time stabilizability of the closed-loop system and the settling time is estimated. Accordingly, some criteria for the finite-time instabilizability are also established by adjusting different parameters in the designed controller. Finally, several numerical simulations are given to show the effectiveness and advantages of the proposed results.

Admissibility analysis and control synthesis for nonlinear discrete-time singular systems are considered in this article. With regard to the type-1 and interval type-2 fuzzy singular systems, the partition of membership functions and scale transform is imposed, and new switched fuzzy systems, which are equivalent to the original systems, are established. A relaxed stability criterion is derived to ensure the admissibility of the system by using the piecewise Lyapunov function and singular value decomposition. Moreover, two classes of switched controllers are designed for the systems. One is for type 1 systems and the membership functions are consistent with those of the systems. The other can be applied to both of the fuzzy systems by introducing linear membership functions in each subregion. Two criteria are obtained to guarantee that the closed-loop systems are admissible. Several illustrative examples are provided to show the effectiveness of the developed methods.

This article focuses on the fixed-time pinning common synchronization and adaptive synchronization for quaternion-valued neural networks with time-varying delays. First, to reduce transmission burdens and limit convergence time, a pinning controller which only controls partial nodes directly rather than the entire nodes is proposed based on fixed-time control theory. Then, by Lyapunov function approach and some inequalities techniques, fixed-time common synchronization criterion is established. Second, further to realize the self-regulation function of pinning controller, an adaptive pinning controller which can adjust automatically the control gains is developed, the desired fixed-time adaptive synchronization is achieved for the considered system, and the corresponding criterion is also derived. Finally, the availability of these results is tested by simulation example.