Switching using distributed delays

Abstract

Control systems for which are known two stabilizing controllers are considered. They respectively globally asymptotically and locally asymptotically stabilize the origin. The objective pursued in this work is the determination, when possible, of a so-called uniting controller i.e. a control law which, on the one hand, renders the origin globally attractive and, on the other hand, is such that, along all trajectories, the global control law is used before some time-instant, and, after a larger time-instant, the local control law is used. In a recent paper it is established that in general the uniting problem cannot be solved by using a continuous static time-invariant state feedback without delay. In this paper, it is shown that the uniting problem can be solved through continuous distributed delay control laws.