On the stabilizability of multiple integrators by means of bounded feedback controls

Abstract

It is known that a linear system x = Ax + Bu canbe stabilized by means of a smooth bounded control ifand only if it has no eigenvalues with positive real part,and all the uncontrollable modes have negative realpart. Here we investigate, for single-input systems,the question whether such systems can be stabilized bymeans of a feedback u = oe(h(x)), where h is linear andoe(s) is a saturation function such as sign(s) min(jsj; 1).A stabilizing feedback of this particular form exists ifA ...