Exponential Stability, Passivity, and Dissipativity Analysis of Generalized Neural Networks With Mixed Time-Varying Delays

In this paper, we analyze the exponential stability, passivity, and <inline-formula> <tex-math notation="LaTeX">$\boldsymbol {(\mathfrak {Q},\mathfrak {S},\mathfrak {R})}$ </tex-math></inline-formula>-<inline-formula> <tex-math notation="LaTeX">$\boldsymbol {\gamma }$ </tex-math></inline-formula>-dissipativity of generalized neural networks (GNNs) including mixed time-varying delays in state vectors. Novel exponential stability, passivity, and <inline-formula> <tex-math notation="LaTeX">$\boldsymbol {(\mathfrak {Q},\mathfrak {S},\mathfrak {R})}$ </tex-math></inline-formula>-<inline-formula> <tex-math notation="LaTeX">$\boldsymbol {\gamma }$ </tex-math></inline-formula>-dissipativity criteria are developed in the form of linear matrix inequalities for continuous-time GNNs by constructing an appropriate Lyapunov-Krasovskii functional (LKF) and applying a new weighted integral inequality for handling integral terms in the time derivative of the established LKF for both single and double integrals. Some special cases are also discussed. The superiority of employing the method presented in this paper over some existing methods is verified by numerical examples.

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