Design of generalized dissipativity state estimator for static neural networks including state time delays and leakage delays

Abstract This paper discusses the issue of generalized dissipativity index for state estimation of static neural networks (SNNs) including leakage delays and state time delays. The integral terms in the time derivative of the Lyapunov–Krasovskii functionals (LKFs) are estimated by the well-known Wirtinger based integral inequality approach. As a result, a novel delay-dependent extended dissipativity state estimation condition is exploited based on the estimated error system is extended dissipative. The notion of the extended dissipativity based state estimation methodology is launched to investigate the L 2 − L ∞ state estimation, H ∞ state estimation, passivity state estimation, mixed H ∞ and passivity state estimation, and ( Q , S , R ) − γ -dissipativity state estimation of SNNs by choosing free weighting matrices. Therefore, a new scheme is put forward to quantify multi-dynamic behaviors of SNNs in a combined structure by introducing of the free weighting matrices. The main scope of the addressed problem is to design state estimation criterion to estimate the neuron states such that, in the presence of both leakage delays and state time delays, the dynamics of the estimator error system is extended dissipative. In comparison with some recent results, much better and more dynamic behavior is performed by our methodology, which is immensely assisted from proposing a leakage delays and gain matrix in the system model. The advantage of the established methodology is explored by numerical examples and comparison results also are made along with the previous results.