LMI-Based Approach for Global Asymptotic Stability Analysis of Recurrent Neural Networks with Various Delays and Structures

Abstract

Global asymptotic stability problem is studied for a class of recurrent neural networks with distributed delays satisfying Lebesgue-Stieljies measures on the basis of linear matrix inequality. The concerned network model includes many neural network models with various delays and structures as its special cases, such as the delays covering the discrete delays and distributed delays, and the network structures containing the neutral-type networks and high-order networks. Therefore, many new stability criteria for the above neural network models have also been derived from the present stability analysis method. All the obtained stability results have similar matrix inequality structures and can be easily checked. Three numerical examples are used to show the effectiveness of the obtained results.

Observer-Based State Estimation for Recurrent Neural Networks: An Output-Predicting and LPV-Based Approach

“…Over the past decades, delayed recurrent neural networks were successfully applied in many fields, including pattern recognition, image processing, and combinatorial optimization [1][2][3][4][5], and the dynamic behaviors of RNNs have quickly become a research hotspot. At present, many stability results about the dynamic behavior of RNNs have been obtained [6][7][8][9][10][11][12]. Meanwhile, the state information of neurons is very important, because it may participate in the design process of control law, such as feedback control.…”

Novel Stochastic Stability Conditions of Fuzzy Neural Networks With Markovian Jumping Parameters Under Impulsive Perturbations

“…In practice, due to the finite speeds of the switching and transmission of signals, time delays do exist in a working network and thus should be incorporated into the model equation. In recent years, the dynamical behaviors of cellular neural networks with constant delays or timevarying delays or distributed delays have been studied by many researchers; see, for example, [7,9,10,18,19,23,24,28,30] and the references therein.…”