On robust stability of time-variant discrete-time nonlinear systems with bounded parameter perturbations

The upper and lower bounds for asymptotic stability (AS) of a time-variant discrete-time nonlinear system with bounded parameter perturbations are provided. The analysis is undertaken for a class of nonlinear relaxation systems with the saturation nonlinearity of sigmoid type. Based upon the theory of convex polytopes and underlying linear relaxation equation, the bounds of the stability region for such a nonlinear system are derived for every time instant.