Dissipativity of discrete-time BAM stochastic neural networks with Markovian switching and impulses

Robust passivity analysis for stochastic impulsive neural networks with leakage and additive time-varying delay components

“…It is well known that the dissipativity theory plays an important role in the stability analysis of dynamical systems, nonlinear control and other areas (see,e.g., [5][6][7][8][9][10][11][12][13][14][15][16] and the references therein). Passivity, as a special case of dissipativity, tells more than just stability, which relates the input and output to the storage function, and hence defines a set of useful input-output properties.…”

“…Some stochastic input could destabilize a neural network. Therefore, the stability problem for stochastic networks with time delay becomes more important from the practical point of view, see, for instance [8,[10][11][12][13][14][15]20,22,25,28,30,31,44]. Recently, a special type of time delay, namely, leakage delay (or forgetting delay), is identified and investigated due to its existence in many real systems such as neural networks, population dynamics, control systems and some fuzzy systems such as in [10,[16][17][18][19][20][21]24,25,44].…”

“…Impulsive phenomenon, as well as time delays, can influence the dynamical behavior of the neural networks. Therefore, it is more important to study the stability of delayed neural networks with impulsive perturbations for instance can see related impulsive problems have been existing in literature, see [15,[22][23][24][25][26][27][28][29][30][31]44].…”

Global Stability and Synchronization of Markovian Switching Neural Networks with Stochastic Perturbation and Impulsive Delay

“…In [17], almost sure exponential stability was researched for recurrent neural networks with Markovian switching. In [14], dissipativity of discrete-time bidirectional associative memory (BAM) stochastic neural networks with Markovian switching and impulses was investigated.…”

“…Besides stochastic perturbation, impulsive effects also exist in neural networks [10,12,14,22,23,31,32]; For instance, in the implementation of electronic networks, the state of the network is subject to instantaneous perturbations and experiences abrupt change at certain instances, which may be caused by switching phenomena, frequency changes, or sudden noise. In [23], synchronization of delayed complex dynamical networks with impulsive and stochastic effects was investigated.…”