Effect of fuzziness on the stability of inertial neural networks with mixed delay via non-reduced-order method

ABSTRACT In this paper, without transforming the original inertial neural networks into the first-order differential equation by some variable substitutions, fuzziness, time-varying and distributed delays are introduced into inertial networks and the existence, the uniqueness and the asymptotic stability for the neural networks are investigated. The existence of a unique equilibrium point is proved by using inequality techniques, and the properties of an M-matrix. By finding a new Lyapunov–Krasovskii functional, some sufficient conditions are derived ensuring the asymptotic stability. Finally, three numerical examples with simulation are presented to show the effectiveness of our theoretical results.