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In this paper,a novel non-monotonic Lyapunov-Kra-sovskii functional approach is proposed to deal with the stability analysis and stabilization problem of linear discrete time-delay systems.This technique is utilized to relax the monotonic require-ment of the Lyapunov-Krasovskii theorem.In this regard,the Lyapunov-Krasovskii functional is allowed to increase in a few steps,while being forced to be overall decreasing.As a result,it relays on a larger class of Lyapunov-Krasovskii functionals to provide stability of a state-delay system.To this end,using the non-monotonic Lyapunov-Krasovskii theorem,new sufficient conditions are derived regarding linear matrix inequalities(LMIs)to study the global asymptotic stability of state-delay systems.Moreover,new stabilization conditions are also proposed for time-delay systems in this article.Both simulation and experi-mental results on a pH neutralizing process are provided to demonstrate the efficacy of the proposed method.