A Sliding Surface Design for Linear Systems with Mismatched Uncertainties based on Linear Matrix Inequality

Sliding mode control (SMC) is an effective method of controlling systems with uncertainties which satisfy the so-called matching condition. However, how to effectively handle mismatched uncertainties of systems is still an ongoing research issue in SMC. Several methods have been proposed to design a stable sliding surface even if mismatched uncertainties exist in a system. Especially, it is presented that robustness and efficiency of SMC for linear systems with mismatched uncertainties can be improved by reducing mismatched uncertainties in the reduced-order system. The reduction method needs a new sliding surface with an additional component based on Lyapunov redesign technique. In this paper, a stable sliding surface which contains additional component to reduce the influence of mismatched uncertainties, is introduced. It is designed by using linear matrix inequalities that guarantees the stability of the system. A numerical example demonstrates the validity of the proposed scheme.