Hyperplane design in variable structure control of descriptor systems

This paper is concerned with variable structure systems (VSS) for descriptor systems; in particular it includes the design of the hyperplane, on which a stable sliding mode occurs, is described in detail. The authors propose for linear descriptor systems a hyperplane from which, on the basis of a Lyapunov function, a sufficient condition of the control gain to stabilize the system is derived. Two methods of designing switching hyperplanes are presented. The first one is derived from a parametric eigenstructure assignment of descriptor systems. The second one is based on a geometric approach using the projector theory. The regularity requirement of the closed-loop is considered in both methods. Finally, a numerical example is presented to show the potential of the first method