Design of extended dissipativity state estimation for generalized neural networks with mixed time-varying delay signals

Abstract

This paper investigates the issue of extended dissipativity state estimation of generalized neural networks (GNNs) with mixed time-varying delay signals. The integral terms in the time derivative of the Lyapunov–Krasovskii functionals (LKFs) are estimated by the famous Jensen’s inequality, reciprocally convex combination (RCC) approach together with the Wirtinger double integral inequality (WDII) technique. In addition, in order to estimate the double integral terms in the derivative of the LKF, a new integral inequality is proposed. As a result, a new delay-dependent criterion is derived under which the estimated error system is extended dissipative. The concept of extended dissipativity state estimation can be applied to deal with the L2−L∞ state estimation, H∞ state estimation, passivity state estimation, mixed H∞ and passivity state estimation, (Q,S,R)−γ-dissipativity state estimation of GNNs by choosing the weighting matrices. The advantage of the proposed method is demonstrated by five numerical examples, among them one example was supported by real-life application of the benchmark problem that is associated with reasonable issues in the sense of an extended dissipativity performance.