Stability Analysis Of Time Delay Neural Networks Based On The Partitioning Method

The time-delay is inevitable in the application field of neural network, mainly caused by the finite speed of information transmission between neurons and the switch features of circuit system. Because of the existence of time delay often cause poor performance of control systems, even leads to instability. Therefore, the stability analysis of the time-delay neural network systems has important significance.The objects of our research are mainly two typical neural networks with time-varying delays, one is cellular neural networks with time-varying delays and another one is recurrent neural networks with time-varying delays, then their stability are studied and analyzed in this paper. By constructing suitable Lyapunov functional, some new improved delay-dependent stability condition which have less conservative compared with the results of the newly-published papers are derived by combing with the integral inequality method (including Jensen inequality and Wirtinger inequality), reciprocally convex optimization method and partitioning method for the bounding condition of neural activation function, and so on. The main contents are as followed:(1) The cellular neural networks with time-varying delays is studied, we propose a common partitioning method for the bounding of activation function conditions, and utilizing this method to study and analysis the delay-dependent stability criteria of such systems. Firstly, a Lyapunov functional with new variables is constructed and the cross-term relationships with sufficient information are constructed by introducing these new variables. Then, some new improved stability criteria expressed in terms of linear matrix inequalities (LMIs) are derived by employing the combination of Wirtinger inequality and reciprocally convex optimization method. Application our new criteria to two well-known examples show the effectiveness of the proposed results.(2) The delay-partitioning method combined with the bounding of activation function conditions partitioning method is utilizing to futher study and analysis the delay-dependent stability of cellular neural networks with time-varying delay. By decomposing the delay interval into two equal subintervals, adding the appropriate variables to the corresponding term, and enriching the cross-term relationships between different variables, then, we construct an appropriate Lyapunov functional. Furthermore, some new improved delay-dependent stability criteria which have less conservatism than the recent exitsing ones are derived by employing the combination of Wirtinger inequality and reciprocally convex optimization method to handle the time derivative of Lyapunov functional. Finally, we also use two numerical examples to indicate the effectiveness and superiority of our results.(3) The delay-dependent stability problem for recurrent neural networks with time-varying delays is studied. First, by constructing a dedicated Lyapunov-Krasovskii functional (LKF), utilizing the combined method of Wirtinger inequality and reciprocally convex optimization method and convex combination approach, a new improved delay-dependent stability criterion expressed in terms of linear matrix inequalities is derived. Second, using the new partitioning method for bounding conditions on the activation function, further improved delay-dependent stability criterion is established. Finally, application of these novel results to an illustrative example in the literature has been investigated and their effectiveness shown via comparison with the recent existing ones.