On the existence of linear sliding surfaces for a class of uncertain dynamic systems with mismatched uncertainties

Recently, Choi (1998, Automatica, 34 (8), 1015-1020) has considered the pro blem of designing a variable structure control (VSC) law for uncertain syst ems where the uncertainty in the state model does not satisfy the matching condition. He has given a sufficient condition for the existence of linear sliding surfaces in terms of LMIs. In this note, we show that the LMI exist ence condition given in the above paper is a necessary and sufficient one. And, we give LMI existence conditions of a sliding surface guaranteeing gen eral LMI regional pole placement constraints while in the above paper pole placement only in a vertical half-plane and a disk has been considered. Fin ally, we give simulation results for controlling an inverted pendulum mount ed on a cart. (C) 1999 Elsevier Science Ltd. All rights reserved.