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This paper is concerned with the passivity problem for neural networks with leakage delay and time-varying transmission delay. Using some novel Lyapunov-Krasovskii (L-K) functionals, and combining with the Wirtinger integral inequality, some less conservative delay-dependent passivity conditions are proposed in terms of linear matrix inequalities (LMIs). Different from the existing approaches, the model transformation is abandoned in this paper, and the proposed L-K functionals incorporate the interconnected terms related to both the leakage delay and the time-varying delay. Numerical examples show that the obtained conditions are less conservative. [ABSTRACT FROM AUTHOR]

This paper is concerned with the l 2 − l ∞ state estimation problem for discrete-time switched neural networks with time-varying delay. The main objective is to design a mode-dependent state estimator such that the error dynamics is exponentially stable with a weighted l 2 − l ∞ performance level. By incorporating the novel l 2 − l ∞ performance analysis approach, the augmented piecewise Lyapunov-like functionals, the discrete Wirtinger-based inequality and the average-dwell-time switching, less conservative sufficient conditions are proposed by means of linear matrix inequalities. A numerical example is given to illustrate the effectiveness and benefits of the obtained results. [ABSTRACT FROM AUTHOR]