LMI approach for global periodicity of neural networks with time-varying delays

This paper investigates the global periodicity of neural networks with time-varying delays. Several conditions guaranteeing the existence, uniqueness, and global asymptotical and exponential stability of periodic solution are obtained. These criteria are expressed in terms of linear matrix inequalities, thus they can be efficiently verified. Moreover, according to the criteria, the maximal bound of time delays and the fastest convergence speed can also be estimated for the exponential periodicity of neural networks. Some examples are given to illustrate the effectiveness of the given criteria.