Improved global robust stability of interval delayed neural networks via split interval: Generalizations

The problem of global robust stability of Hopfield-type delayed neural networks with the intervalized network parameters is revisited. Recently, a computationally tractable, i.e., linear matrix inequality (LMI) based global robust stability criterion derived from an earlier criterion based on dividing the given interval into more that two intervals has been presented. In the present paper, generalizations, i.e., division of the given interval into m intervals (where m is an integer greater than or equal to 2) is considered and some new LMI-based global robust stability criteria are derived. It is shown that, in some cases, m = 2 may not suffice, i.e., m > 2 may be needed to realize the improvement. An example showing the effectiveness of the proposed generalization is given. The paper also provides a complete and systematic explanation of the “split interval” idea.