Further extensions on a stability property with slowly varying inputs

Abstract

In this paper we present three extended results on the stability property with slowly varying inputs that has been studied in, e.g., Khalil and Kokotovíc (1991). The stability property has played an important role in control methodologies such as gainscheduling controls or robust controls for systems having slowly varying parameters. We begin with a review of the first extension, which shows that the inputs may vary fastly, but once its 'average' is slowly varying, then the same stability property still holds. The second extension deals with the case when a (transcritical) bifurcation occurs so that the assumptions of the stability property are violated. We propose a Jump & Wait strategy which will still guarantee the stability property even under this case. Finally we prove that the Jump & Wait strategy can be employed not with the input itself but with the average of the input if the proposed structural condition is satisfied. Copyright © 2010 Watam Press.