Semi-global exponential stabilization of linear systems subject to “input saturation” via linear feedbacks

Abstract

It is known that a linear time-invariant system subject to “input saturation” can be globally asymptotically stabilized if it has no eigenvalues with positive real parts. It is also shown by Fuller (1997) and Sussmann and Yang (1991) that in general one must use nonlinear control laws and only some special cases can be handled by linear control laws. In this paper we show the existence of linear state feedback and/or output feedback control laws for semi-global exponential stabilization rather than global asymptotic stabilization of such systems. We explicitly construct linear static state feedback laws and/or linear dynamic output feedback laws that semi-globally exponentially stabilize the given system. Our results complement the “negative result” of Fuller (1977) and Sussmann and Yang (1991).