An explicit formula of linear sliding surfaces for a class of uncertain dynamic systems with mismatched uncertainties

In this note, the problem of designing a variable structure control (VSC) law for uncertain systems where the uncertainty in the state model does not satisfy the matching condition is considered. Based on the LMI approach we develop a new design method of linear sliding surfaces which are linear to the state. We give a sufficient condition for the existence of linear sliding surfaces in terms of LMIs and we give an explicit formula of linear sliding surfaces guaranteeing the quadratic stability of the reduced-order equivalent system dynamics restricted to the sliding surfaces. We also give sufficient conditions for the existence of linear sliding surfaces insuring some pole clustering constraints. Thus, one can easily design VSC laws for a class of uncertain systems with mismatched uncertainties which are difficult to deal with by using conventional VSC design methods. Finally, we give a design example. (C) 1998 Elsevier Science Ltd. All rights reserved.