4.6 Article

Energy-to-Peak State Estimation for Static Neural Networks With Interval Time-Varying Delays

Journal

IEEE TRANSACTIONS ON CYBERNETICS
Volume 48, Issue 10, Pages 2823-2835

Publisher

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TCYB.2018.2836977

Keywords

Energy-to-peak state estimation; integral inequality; interval time-varying delay; static neural networks (SNNs)

Funding

  1. Australian Research Council Discovery Project [DP160103567]
  2. National Natural Science Foundation of China [61733016, 61503351, 51428702, 61573325, 61773356]
  3. Hubei Provincial Natural Science Foundation of China [2015CFA010]
  4. 111 Project [B17040]

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This paper is concerned with energy-to-peak state estimation on static neural networks (SNNs) with interval time-varying delays. The objective is to design suitable delay-dependent state estimators such that the peak value of the estimation error state can be minimized for all disturbances with bounded energy. Note that the Lyapunov-Krasovskii functional (LKF) method plus proper integral inequalities provides a powerful tool in stability analysis and state estimation of delayed NNs. The main contribution of this paper lies in three points: 1) the relationship between two integral inequalities based on orthogonal and nonorthogonal polynomial sequences is disclosed. It is proven that the second-order Bessel-Legendre inequality (BLI), which is based on an orthogonal polynomial sequence, outperforms the second-order integral inequality recently established based on a nonorthogonal polynomial sequence; 2) the LKF method together with the second-order BLI is employed to derive some novel sufficient conditions such that the resulting estimation error system is globally asymptotically stable with desirable energy-to-peak performance, in which two types of time-varying delays are considered, allowing its derivative information is partly known or totally unknown; and 3) a linear-matrix-inequality-based approach is presented to design energy-to-peak state estimators for SNNs with two types of time-varying delays, whose efficiency is demonstrated via two widely studied numerical examples.

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