This paper addresses the problem of ℋ∞ finite-time boundedness for discrete-time neural networks with interval-like time-varying delays. First, a delay-dependent finite-time boundedness criterion under the finite-time ℋ ∞ performance index for the system is given based on constructing a set of adjusted Lyapunov–Krasovskii functionals and using reciprocally convex approach. | VNU Journal of Science Mathematics Physics Vol. 36 No. 3 2020 10-23 Original Article ℋ Finite-time Boundedness for Discrete-time Delay Neural Networks via Reciprocally Convex Approach Le Anh Tuan Department of Mathematics University of Sciences Hue University 77 Nguyen Hue Hue Vietnam Received 25 May 2020 Revised 07 July 2020 Accepted 15 July 2020 Abstract This paper addresses the problem of ℋ finite-time boundedness for discrete-time neural networks with interval-like time-varying delays. First a delay-dependent finite-time boundedness criterion under the finite-time ℋ performance index for the system is given based on constructing a set of adjusted Lyapunov Krasovskii functionals and using reciprocally convex approach. Next a sufficient condition is drawn directly which ensures the finite-time stability of the corresponding nominal system. Finally numerical examples are provided to illustrate the validity and applicability of the presented conditions. Keywords Discrete-time neural networks ℋ performance finite-time stability time-varying delay linear matrix inequality. 1. Introduction In recent years neural networks NNs have received remarkable attention because of many successful applications have been realised . in prediction optimization image processing pattern recognization association memory data mining etc. Time delay is one of important parameters of NNs and it can be considered as an inherent feature of both biological NNs and artificial NNs. Thus analysis and synthesis of NNs with delay are important topics 1-3 . It is worth noting that Lyapunov s classical stability deals with asymptotic behaviour of a system over an infinite time interval and does not usually specify bounds on state trajectories. In certain situations finite-time stability initiated from the first half of the 1950s is useful to study behaviour of a system within a finite time interval maybe short . More precisely those are situations that state ____ Corresponding author Email
