On H∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${H}_\\infty $$\\end{document} Finite-Time Boundedness and Finite-Time Stability for Discrete-Time Neural Networks with Leakage Time-Varying Delay

Abstract

This paper investigates the problems of H∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H_\\infty $$\\end{document} finite-time boundedness (FTB) and finite-time stability (FTS) for discrete-time neural networks (NNs) with both leakage delay and discrete delay, as well as different generalized activation functions. To this end, we construct suitable Lyapunov–Krasovskii (L–K) functionals and apply the extended reciprocally convex approach to derive delay-dependent criteria for the addressed problems. The obtained conditions are expressed as linear matrix inequalities (LMIs), which can be efficiently solved by the LMI Toolbox in Matlab. The paper also admits of two numerical examples to point up the advantages and reliability of the proposed method.