Improved Results on $$L_2-L_\infty $$ L 2 - L ∞ State Estimation for Neural Networks with Time-varying Delay

This paper focuses on the problem of $$L_2-L_\infty $$ state estimation for neural networks with time-varying delay. An improved $$\alpha ^{2}$$ -dependent reciprocally convex inequality is proved. Combining the suitable augmented Lyapunov–Krasovskii functionals with the generalized free-weighting-matrix integral inequality, the Bessel–Legendre inequality and this novel $$\alpha ^{2}$$ -dependent reciprocally convex matrix inequality, two less conservative state estimation criteria with $$L_2-L_\infty $$ (or called energy-to-peak ) performance are established. Finally, some numerical examples are provided to illustrate the effectiveness and benefits of our proposed approach.