Abstract
We investigate state estimation for a class of discrete-time recurrent neural networks with leakage delay and time-varying delay. The design method for the state estimator to estimate the neuron states through available output measurements is given. A novel delay-dependent sufficient condition is obtained for the existence of state estimator such that the estimation error system is globally asymptotically stable. Based a novel double summation inequality and reciprocally convex approach, an improved stability criterion is obtained for the error-state system. Two numerical examples are given to demonstrate the effectiveness of the proposed design methods. The simulation results show that the leakage delay has a destabilizing influence on a neural network system.
Highlights
Neural networks have become a hot research topic in the past few years, and many problems such as feedback control [ ], stability [ – ], dissipativity and passivity [ – ] are being taken to treat in various dynamic neural networks systems
The state estimation problem is studied for neural networks with timevarying delays in [ ]
A sufficient condition is obtained such that the error estimate system for discrete-time bidirectional associative memory (BAM) neural networks is globally exponentially stable in [ ]
Summary
Neural networks have become a hot research topic in the past few years, and many problems such as feedback control [ ], stability [ – ], dissipativity and passivity [ – ] are being taken to treat in various dynamic neural networks systems. The major contributions of this paper can be summarized as follows: ( ) A state estimator and a delay-dependent stability criterion for the error system of discrete-time neural networks with leakage delay in terms of linear matrix inequalities (LMIs) are developed. An} is the state feedback matrix with entries |ai| < , W ∈ Rn×n and W ∈ Rn×n are the interconnection weight matrices, J denotes an external input vector, y(k) ∈ Rm is the measurement output, φ(k, ·) is the neuron-dependent nonlinear disturbance on the network outputs, C is a known constant matrix of appropriate dimension, τ (k) denotes the time-varying delay satisfying < τ ≤ τ (k) ≤ τ , where τ , τ are known positive integers, and σ is a known positive integer representing the leakage delay.
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