Stability Criteria For Networks With Time-delay

Stability is one of hotspots of researchs on real-valued neural networks and complex-valued neural networks. Recently, many researchers begin to study complex-valued neural networks, and their commom goals are exploring new capabilities and higher performance of this kinds of neural networks. As to research on the stability of real-valued ones, special activation functions such as inverse Lipschitz neuron activations are introduced to analyze the stability of the networks.The main results and innovations are listed as following.Firstly, the global asymptotically stability of a kind of networks with time-varying delays and inverse Lipschitz activations is presented. And several sufficient conditions are also established to ensure the balance point uniquely existing and the property of global asymptotically stability of the equilibrium point in this kind of networks. In [21] and [25] the authors studied the neural networks with inverse Lipschitz activations function, but they didn't consider time-delay,so the results in this paper improve the works in [21] and [25].Secondly, we got some complex-valued linear matrix inequality which can be thought as generalizations of real-valued matrix inequality.Thirdly, boundedness and stability of discrete-time delayed neural network is inverstegated. For complex-valued uncertain neural network with discrete and distributed time-delays, it's global robust stability criteria is reseached. By constructing appropriate Lyapunov-Krasovskii functionals and employing linear matrix inequality technique and analysis method, several new delay-dependent criteria for checking the boundedness, global exponential stability and global robust exponential stability are established. At last illustrated example is also given to show the effectiveness of the proposed criteria. Compared with [48], [49], we not only consider time-delays, time-varying, time-delays, distributed time-delays and uncertain parameter, but also relaxed the requirement of connection weight matrix.