Global exponential stabilization of impulsive neural networks with unbounded continuously distributed delays

Globally exponential stabilization of neural networks with mixed time delays via impulsive control

“…On the other hand, it seems that condition (3) cannot be removed if we want to achieve exponential stability. In fact, all the existing results concerning exponential stability of INNs with unbounded distributed delays impose condition (3) on the delay kernels, see, for example, [33,35,36,[38][39][40][41][42][43]46,47] and the references therein.…”

“…With the help of standard numerical software, the desired gains can be achieved by solving the corresponding LMIs. It is worth mentioning that the impulsive controller synthesis problem is not considered in [43].…”

“…In the recent literatures, effects of impulses on stability of neural networks with various time delays have received a great deal of attention. For example, stability properties of INNs with bounded delays have been investigated in [22][23][24][25][26][27][28][29][30][31][32], and the stability problem of the INNs with unbounded distributed delays has been considered in [33][34][35][36][37][38][39][40][41][42][43]. In general, impulses are roughly classified into three categories: stabilizing impulses, destabilizing impulses and "neutral"-type impulses.…”

“…However, stability criteria for stabilizing impulses in [22][23][24][25][26][27] only dealt with neural networks with bounded delays. Moreover, among those references mentioned above, only the results in [41][42][43] are devoted to stability analysis for neural networks with unbounded distributed delays and stabilizing impulses. In [41,42], the stabilizing effects of impulses were investigated by using the Lyapunov-Razumikhin method.…”

“…In [41,42], the stabilizing effects of impulses were investigated by using the Lyapunov-Razumikhin method. In [43], by establishing an impulsive delay differential inequality, some sufficient conditions for exponential stability caused by impulses were presented. It should be pointed out that all the results in [41][42][43] are not suitable to solve the synthesis problem of the following linear impulsive controller:…”