Improved criteria of delay-dependent stability for discrete-time neural networks with leakage delay

Asynchronous H∞ control of Markov jump discrete-time systems with incomplete transition probability and unreliable links

In this study, an asynchronous H_∞ state feedback controller is devised for Markov jump discrete-time systems (MJDTSs) with time-varying delay. "Asynchronous" means that the system switching mode θ_k, the controller mode ϑ_k and the quantizer mode λ_k are different from each other. The first one is homogeneous and the last two are non-homogeneous. In particular, as a promotion of existing work, we firstly attempt to propose the transition probabilities (TPs) of the three Markov chains (MCs) are not completely known. In addition, the discrete time-varying delay and its infinitely distributed ones are considered. Moreover, according to the Lyapunov stability theory and stochastic process, it is established for the sufficient criterion to ensure the stochastic stability of resulting closed-loop MJDTSs with an H_∞ attenuation performance index. The feasibility and effectiveness of the proposed method are validated by three examples.

Multistability and attraction basins of discrete-time neural networks with nonmonotonic piecewise linear activation functions

This paper is concerned with multistability and attraction basins of discrete-time neural networks with nonmonotonic piecewise linear activation functions. Under some reasonable conditions, the addressed networks have (2m+1)ⁿ equilibrium points. (m+1)ⁿ of which are locally asymptotically stable, and the others are unstable. The attraction basins of the locally asymptotically stable equilibrium points are given in the form of hyperspherical regions. These results here, which include existence, uniqueness, locally asymptotical stability, instability and attraction basins of the multiple equilibrium points, generalize and improve the earlier publications. Finally, an illustrative example with numerical simulation is given to show the feasibility and the effectiveness of the theoretical results. The theoretical results and illustrative example indicate that the activation functions improve the storage capacity of neural networks significantly.