Ultimate Boundedness Sets for Continuous-time Linear Systems with Deadzone Feedback Controls

This paper is concerned with the construction of positively invariant convex polyhedral uniform ultimate boundedness sets for linear continuous-time systems with stabilizing deadzone feedback control laws. The objective is delimitation and region of attraction estimation of possible limit cycles around origin of open-loop unstable systems. Limit cycle delimitation is performed via construction of a positively invariant convex compact polyhedral estimate of the minimal positively invariant set containing an arbitrarily small neighborhood of origin. Region of attraction estimation is performed via construction of a piecewise-affine Lyapunov function assuring uniform ultimate boundedness in the above mentioned convex positively invariant polyhedral set.