Linear matrix inequality approach to stochastic stability of uncertain delayed BAM neural networks
Rathinasamy Sakthivel, Ramachandran Raja, Selvaraj Marshal Anthoni · IMA Journal of Applied Mathematics · 2012
In this paper, the problem of stochastic stability for a class of neutral-type bi-directional associative memory (BAM) neural networks with Markovian jumping and impulsive effects has been investigated. A generalized activation function is considered, and the traditional assumptions on the boundedness, monotony and differentiability of the activation functions are removed. By introducing a new Lyapunov–Krasovskii functional and employing a combination of the free-weighting matrix method and some inequality techniques, a new set of sufficient conditions is established for achieving the required result. Further, the result is extended to investigate robust stability analysis for BAM neural networks with impulses which contain uncertain parameters with their values being bounded. The obtained conditions are expressed in terms of linear matrix inequalities (LMI) whose feasibility can be checked easily via the MATLAB LMI toolbox. Further, two examples with simulation results are provided to show the effectiveness and less conservatism of the obtained results.