A delay decomposition approach for robust dissipativity and passivity analysis of neutral‐type neural networks with leakage time‐varying delay

Abstract

This article presents the robust dissipativity and passivity analysis of neutral-type neural networks with leakage time-varying delay via delay decomposition approach. Using delay decomposition technique, new delay-dependent criteria ensuring the considered system to be ðQ; R; SÞ-c dissipative are established in terms of strict linear matrix inequalities. A new Lyapunov-Krasovskii functional is constructed by dividing the discrete and neutral delay intervals into m and l segments, respectively, and choosing different Lyapunov functionals to different segments. Further, the dissipativity behaviors of neural networks which are affected due to the sensitiveness of the time delay in the leakage term have been taken into account. Finally, numerical examples are provided to show the effectiveness of the proposed method. V C 2015 Wiley Periodicals, Inc. Complexity 21: [248][249][250][251][252][253][254][255][256][257][258][259][260][261][262][263][264] 2016

Delay-dependent passivity analysis of impulsive neural networks with time-varying delays

“…2, we can know that neural network (22) with input u(t) = (e − 1 2 t , 1 3 e −t ) T can keep internally stable. (e) shows the state curves (x 1 (t), x 2 (t)) of impulsive neural network (22) with zero initial condition. From (f), it shows that the time-series of the states x 1 (t), x 2 (t) of neural network (22) without impulsive effects.…”

“…At the same time, passivity analysis approach has been used in control problems [25][26][27]. In [22,24], the authors investigated the passivity for neural networks of neutral type with time-varying delays in the leakage term by constructing proper Lyapunov-Krasovskii functional. Vembarasan et al [25] discussed the state estimation for delayed genetic regulatory networks (GRNs) based on passivity analysis approach.…”

“…Meanwhile, in many engineering problems, the theory of dissipative systems which postulates the energy dissipated inside a dynamic system is less than the energy supplied from external source often links the stability problems. Passivity is part of a broader and a general theory of dissipativeness [22][23][24].…”

“…The essence of the passivity theory is that the passive properties of a system can keep the system internal stability [13]. Thus, the passivity theory provides a nice tool for analyzing the properties of a nonlinear system, such as stability, signal processing and synchronization, and the passivity analysis has received a lot of attention [14][15][16][17][18][19][20][21][22][23][24][25]. In fact, one remarkable feature of passivity is that the passive system utilizes the product of input and output as the energy provision and embodies the energy attenuation character.…”

Nonfragile passivity and passification of nonlinear singular networked control systems with randomly occurring controller gain fluctuation

“…The key idea of passivity theory is that a passive system can keep itself internally stable [20][21][22][23][24][25][26]. As a result, the passivity and passification problems have been a hot research area in the past years and a lot of applications based on passivity theory can be found in many areas, such as signal processing, stability analyzing, chaos control, and so on [27][28][29][30][31][32]. However, to the best of the authors' knowledge, there is no result addressed on the nonfragile passivity and passification problems of singular NCSs with time-varying delay and randomly occurring controller gain fluctuation, which motivates us for this study.…”