Global asymptotic stability for a class of nonlinear systems which are equivalent to neutral higher order Functional Differential Equations

This paper has a strong motivation in the models occurring in the problem of PIO (Pilot In-the-Loop Oscillations) where any pilot model contains at least one pure delay; at the same time in the so-called PIO II category all dynamics are assumed linear except the position and rate limiters whose models include the saturation nonlinearity - a typical bounded nonlinear function. Interesting enough, an equally motivating application arises from neural networks dynamics where both delays and bounded sigmoids are to be met. In this paper we start from some classical results for integral equations concerning boundedness and asymptotic behavior and extend them to an interesting class of systems whose structure incorporates those described by input/output neutral functional differential equations of higher order.