Global asymptotic stability by complex-valued inequalities for complex-valued neural networks with delays on period time scales

By using Homeomorphism theory and some new inequality techniques, a novel LMI-based sufficient condition on global asymptotic stability of equilibrium point for complex-valued recurrent neural networks with time delays on period time scales is established. In our result, the assumption for boundedness in Song and Zhao (2016) [25] on the complex-valued activation functions is removed and the matrix form of the square terms in Li et al. (2009) [23] and Yang and Li (2015) [24] is replaced with a new matrix form, the complex-valued matrix inequalities in Song and Zhao (2016) [25] and Chen and Song (2013) [26] are replaced with some new matrix inequalities which are derived from two new algebraic inequalities. Hence, our result on global stability is less conservative than those obtained in Song and Zhao (2016) [25] and more novel than those obtained in Li et al. (2009) [23], Yang and Li (2015) [24], Song and Zhao (2016) [25], and Chen and Song (2013) [26].