Output feedback sliding mode design for linear uncertain systems

The paper considers the development of output feedback sliding mode controllers for a class of uncertain linear systems. The presence of stable invariant zeros and matched uncertainty is incorporated in the design procedure. The sufficient conditions for developing static output feedback sliding mode controllers are first reviewed. If the so-called ‘Kimura–Davison’ conditions are not satisfied, it is shown that it may not be possible to determine a static output feedback sliding mode controller. In this case, dynamic output feedback sliding mode control is necessary. It is shown that both the switching surface design problem for the static case and the switching surface and compensator design for the dynamic case may be formulated as a static output feedback problem for particular system triples. A robust design procedure is used to solve this static output feedback problem to minimise the effects of any unmatched uncertainty which will affect the reduced order sliding motion in many practical systems. A controller is synthesised to tolerate matched model uncertainty. The measurements of robustness are described. A numerical example demonstrates the procedure.