Abstract
This paper is concerned with the problem of the guaranteed $\mathcal{H_{\infty}}$ performance state estimation for static neural networks with interval time-varying delay. Based on a modified Lyapunov-Krasovskii functional and the linear matrix inequality technique, a novel delay-dependent criterion is presented such that the error system is globally asymptotically stable with guaranteed $\mathcal{H_{\infty}}$ performance. In order to obtain less conservative results, Wirtinger’s integral inequality and reciprocally convex approach are employed. The estimator gain matrix can be achieved by solving the LMIs. Numerical examples are provided to demonstrate the effectiveness of the proposed method.
Highlights
1 Introduction Neural networks can be modeled either as a static neural network model or as a local field neural network model according to the modeling approaches [, ]
When ≤ h(t) ≤ h, that is, the lower bound of the time-varying delay is, we introduce the Lyapunov-Krasovskii functional as follows:
The estimator gain matrix can be determined by solving the LMIs
Summary
Neural networks can be modeled either as a static neural network model or as a local field neural network model according to the modeling approaches [ , ]. In [ ], by constructing an augmented Lyapunov-Krasovskii functional, the guaranteed H∞ performance state estimation problem of static neural networks with interval time-varying delay was discussed. Remark Based on a Lyapunov-Krasovskii functional with triple integrals involving augmented terms, the guaranteed H∞ performance state estimation problem of static neural networks with interval time-varying delay was investigated in [ ], and a sufficient criterion guaranteeing the globally asymptotical stability of the error system ( ) for a given H∞ performance index was obtained [ ]. Remark The integral inequality method and the free-weighting matrix method are two main techniques to deal with the bounds of the integrals that appear in the derivative of Lyapunov-Krasovskii functional for stability analysis of delayed neural networks. By employing a free-matrix-based integral inequality [ ] or the novel integral inequality in [ ], less conservative results than those obtained in our paper may be further derived
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