Robust input-to-state stability of neural networks with Markovian switching in presence of random disturbances or time delays

This paper establishes input-to-state stability (ISS) and robust ISS of neural networks with Markovian switching (NNwMS). The M matrix algebraic condition for stochastic NNwMS is given; the result is then extended to stochastic time varying delays NNwMS. From the ISS condition of stochastic delayed NNwMS, we get robust ISS of NNwMS in two cases: delay perturbation in diffusion and delay perturbation in drift, respectively. These ISS criteria are readily to be checked only from the parameters of the NNwMS and also ensure exponential stability without input term. The results presented here include neural networks without Markovian switching as special cases. Two numerical examples are given to show the effectiveness of theoretical criteria.