Global Passivity Analysis of Interval Neural Networks with Discrete and Distributed Delays of Neutral Type

Abstract

This paper is concerned with delay-dependent passivity analysis for delayed neural networks (DNNs) of neutral type. We first discuss the passivity conditions for DNNs without uncertainties and then extend this result to the case of interval uncertainties. By partitioning the delay intervals into multiple equidistant subintervals, some appropriate Lyapunov-Krasovskii functionals (LKFs) are constructed on these intervals. Considering these new LKFs and using free-weighting matrix approach, several new passivity criteria are proposed in terms of linear matrix inequalities, which are dependent on the size of the time delay. Finally, five numerical examples are given to illustrate the effectiveness and less conservatism of the developed techniques.

Passivity of uncertain neural networks with both leakage delay and time-varying delay

“…The main idea of passivity theory is that the passive properties of system can keep the system internal stability [14][15][16]. Recently, the passivity theory for delayed neural networks was investigated, some criteria checking the passivity were provided for certain or uncertain neural networks, see [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31] and references therein. In [17,18,20,22,24,26,29,31], authors investigated the passivity of neural networks with time-varying delay, and gave some criteria for checking the passivity of neural networks with timevarying delay.…”

“…In [21,23,25], authors investigated the passivity of neural networks with discrete time-varying delays and distributed time-varying delays. In [27], the neural network with discrete and distributed delays of neutral type was considered, several sufficient conditions for checking the passivity of the considered neural network were obtained. In [28,30], stochastic neural networks with time-varying delays were considered, several sufficient conditions checking the passivity ware obtained.…”

“…In [28,30], stochastic neural networks with time-varying delays were considered, several sufficient conditions checking the passivity ware obtained. It is worth pointing out that the given criteria in [17][18][19][20][21][22][23][24][25][26][27][28][29][30] have been based on the following assumptions: (1) the time-varying delays in [17][18][19][20][21][22][23][24][25][26][27][28][29][30] are continuously differentiable; (2) the derivative of time-varying delay in [17][18][19][20][21] is bounded and is smaller than one; and (3) the activation functions in [18,20,24,26,27] are bounded and monotonically nondecreasing; the activation functions in [19,22,23,25,28] are monotonically nondecreasing. However, time delays can occur in an irregular fashion, and sometimes the time-varying delays are not differentiable.…”

On improved passivity criteria of uncertain neural networks with time-varying delays

“…The main idea of passivity theory is that the passive properties of a system can keep the system internal stability. In this regard, increasing attentions have been paid to delay-dependent passivity analysis of neural networks in recent years [9][10][11][12][13][14]. In [9], the passivity problem of uncertain neural networks with both discrete and distributed time-varying delays was investigated by utilizing free-weighting matrices and the LMI framework.…”

“…Very recently, in [13,14], improved delay-dependent passivity criteria for stochastic neural networks with interval time-varying delays had been proposed. In the literature [7,[9][10][11][12][13][14], an important index for checking the conservatism of delay-dependent passivity criteria is to increase the feasible region of criteria or to get maximum delay bounds such that the concerned neural networks are passive. Therefore, how to choose Lyapunov-Krasovskii's functional and obtain an upper bound of time-derivative of it such that the considered neural networks are passive play key roles to reduce the conservatism of passivity criteria.…”