An iterative approach for the description of null controllable regions of discrete-time linear systems with saturating inputs

In this paper an iterative characterization of the null controllable region for discrete-time linear systems subject to input saturation with unstable eigenvalues is proposed. First an outer estimate of the null controllable region by means of invariant hyperparallelograms is obtained and then an iterated convexification technique is developed. Theoretical developments are supported by some illustrative examples.