Passivity analysis of stochastic time-delay neural networks

Abstract

Passivity analysis of stochastic neural networks with time-varying delays and parametric uncertainties is investigated in this paper. Passivity of stochastic neural networks is defined. Both delayindependent and delay-dependent stochastic passivity conditions are presented in terms of linear matrix inequalities (LMIs). The results are established by using the Lyapunov-Krasovskii functional method. In order to derive the delay-dependent passivity criterion, some free-weighting matrices are introduced. The effectiveness of the method is illustrated by numerical examples.

Fractional Variational Problems Depending on Indefinite Integrals and with Delay

“…This is a field under strong research, namely for optimal control problems, differential equations, biology, etc (see e.g. [10,11,16,17,20,27,30,33]). For some literature on what this paper concerns, we suggest the reader to [2,4,6,8,9,12,18,19,23,31] for fractional variational problems dealing with Caputo derivative, in [3] for Lagrangians depending on fractional integrals, and in [13,21] when presence of indefinite integrals.…”

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 [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. 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,…”

“…However, time delays can occur in an irregular fashion, and sometimes the time-varying delays are not differentiable. In such a case, the methods developed in [17][18][19][20][21][22][23][24][25][26][27][28][29][30] may be difficult to be applied, and it is therefore necessary to further investigate the passivity problem of neural networks with time-varying delays under milder assumptions for the time-varying delays and the activation functions. To the best of the authors knowledge, there is no results on the problem of passivity for uncertain neural networks with leakage delay.…”

Decentralized control of uncertain nonlinear stochastic systems based on DSC

“…Since then, a series of extensions have been made under different assumptions or for different stochastic systems. Many interesting control schemes [9][10][11][12][13][14] have been proposed by using the back-stepping technique to solve the stochastic nonlinear disturbances, such as several SISO systems including tracking control [9,10,22], or timedelay systems [11,12,25], and MIMO systems with decentralized control [13,14] are studied.…”