Stability analysis of discrete-time Markovian jump neural networks with time-varying delays via a new summation inequality

This research focuses on the stability of discrete-time Markovian jump neural networks with time-varying delays. To this aim, a nonorthogonal free-matrix-based summation inequality (NFMSI) is proposed by constructing nonorthogonal polynomials with auxiliary scalars as well as auxiliary vectors. The NFMSI can avoid time-varying delays in the denominator and prevent the loss of some coupling information compared to exiting summation inequalities. Then, an ameliorative stability criterion is derived by utilizing the NFMSI and other estimation method. Finally, the advantage of the obtained stability criterion is demonstrated by a few numerical examples.