Ultimate boundedness sets for discrete-time linear systems with deadzone feedback controls

This paper is concerned with positively-invariant convex polyhedral uniform ultimate boundedness sets for open-loop unstable systems. The objective is the delimitation and region-of-attraction estimation of a possible limit cycle encircling the origin. The delimitation of the limit cycle is performed by constructing a positively-invariant convex compact polyhedral estimate of the minimal positively-invariant set containing an arbitrarily small neighborhood around the origin. Region-of-attraction estimation is performed by constructing a piecewise-affine Lyapunov function assuring uniform ultimate boundedness in the above-mentioned convex positively-invariant polyhedral set