Further results on H∞ state estimation for delayed discrete-time neural networks via activation function-dependent zero equalities

This paper studies the problem of $\mathcal{H}_{\infty}$ state estimation for discrete-time neural networks with a time-varying delay. The activation function is assumed to satisfy a sector-bounded condition. A novel Lyapunov-Krasovskii functional is firstly constructed by considering more information of activation function. Then by employing zero equalities based on activation function and its difference, Jensen’s inequality and reciprocally convex approach to deal with the forward difference of the Lyapunov-Krasovskii functional, a less conservative criterion is derived, which can ensure the globally asymptotical stability of the error system with $\mathcal{H}_{\infty}$ performance. The estimator gain matrix can be obtained by solving linear matrix inequalities. Finally, a numerical example is given to illustrate the effectiveness and superiority of the method.