Passivity and stability analysis of neural networks with time-varying delays via extended free-weighting matrices integral inequality

This paper is concerned with the problem of passivity for uncertain neural networks with time-varying delays. First, the recently developed integral inequality called generalized free-matrix-based integral inequality is extended to estimate further tight lower bound of integral terms. By constructing a suitable augmented LKF, an enhanced passivity condition for the concerned network is derived in terms of linear matrix inequalities (LMIs). Here, the integral terms having three states in its quadratic form is estimated by the proposed Lemma. As special cases of main results, for neural networks without uncertainties, passivity and stability conditions are derived. Through three numerical examples, it will be shown that the developed conditions can promote the level of passivity and stability criteria.