Delay-Dependent Exponential Stability of Cellular Neural Networks with Multi-Proportional Delays

Matrix measure based stability criteria for high-order neural networks with proportional delay

“…delay is proportional to the time) is usually required [23]. Therefore, it is significative to research the unbounded delays neural networks, such as [14,[17][18][19][20][21][22]. In [17], authors address the stability of neural networks with unbounded time-varying delays and with bounded Lipschitz continuous activation functions.…”

“…Proportional delay equation research has attracted many scholars' interests [24][25][26]. Since proportional delay equations are different from other delayed equations, thus most results of the stability for delayed neural networks cannot be directly applied to neural networks with proportional delay, see [11,[20][21][22]. Zhou in [21] studied the dissipativity of cellular neural networks with proportional delays.…”

Novel global exponential stability criteria for hybrid BAM neural networks with proportional delays

“…In an amount of parallel pathways, affected by different materials and topology, there may be some unbounded delays which is proportional to the time, so we should choose proper proportional delays factors according to different cases and adopt proportional delays to characterize these unbounded delays. At present, results of dynamical behaviors for neural networks with proportional delays have a few [20,[23][24][25][26][27][28]. In [23], dissipativity of a class of cellular neural networks (CNNs) with proportional delays was investigated by using the inner product properties.…”

“…In [23], dissipativity of a class of cellular neural networks (CNNs) with proportional delays was investigated by using the inner product properties. Zhou in [24][25][26] had discussed the global exponential stability of CNNs with multi-proportional delays by employing matrix theory and constructing Lyapunov functional, respectively. Delay-dependent exponential synchronization of recurrent neural networks with multiple proportional delays was studied in [27] by constructing appropriate Lyapunov functional, several new delay-dependent and decentralized control laws, which are related to the size of the proportional delay factors, were derived to achieve the exponential synchronization.…”

Global asymptotic stability of CNNs with impulses and multi‐proportional delays

“…However, proportional delays are unbounded time‐varying ones different from constant delays , bounded time‐varying delays , and unbounded distributed delay . It is relatively difficult to deal with this class of the unbounded time‐varying delays because none of any other assumptions are imposed on it compared with other unbounded time‐varying delays such as unbounded distributed delays often require that the delay kernel functions satisfy or there exists a positive numbers μ such that .…”