Stability guaranteed sliding controller design subject to low gain switching

When constructing conventional sliding control law, it is well known that the magnitude of a particular discontinuous control effort must be chosen sufficiently large to counteract any mismatch between the model used for controller design and the real system. However, this usually leads to conservative designs with strong discontinuity appearing in the control signals. Techniques are available to smooth the discontinuity, but these cause performance degradations. In addition for an arbitrary given small switching gain, the approaching phase might not be fulfilled immediately and thus the system stability might not be guaranteed. Consequently, this paper develops a stability guaranteed sliding controller subject to light and size-fixed switching effort. The design problem is formulated as certain constrained feasibility problems, which are solved by using linear matrix inequalities (LMIs). Therefore, high gain behavior can be avoided. By using the low gain based sliding controller, prescribed sliding modes can be attained in finite time for any arbitrary given initial positions.