On the limitations of some variable structure output feedback controller designs

Numerical methods to design control laws based on output information only, which ensure a sliding mode is attained, have recently been proposed in the literature. This paper shows that the proposed methods are only applicable to certain classes of linear systems. It is further shown that even if the system has the required structure, then the numerical methods will only terminate satisfactorily for a specific class of switching surface. Although the class of systems for which the schemes are applicable cannot be identified explicitly, a straightforward test can be applied which parameterises all possible appropriate hyperplanes. The theoretical results are illustrated by numerical design studies taken from the relevant literature. (C) 2000 Elsevier Science Ltd. All rights reserved.