Design of sliding mode controllers with bounded L 2 gain performance: an LMI approach

This paper is devoted to the design of robust controllers for sliding mode control systems. A linear fractional transformation (LFT) framework is adopted to describe the systems subject to model uncertainties and external disturbances. A linear matrix inequality (LMI) technique is then developed into the design of both sliding mode and reaching phase control laws. It is shown that by solving a set of LMIs, the switching surface can be designed such that the dynamics in the sliding mode achieve robust stability and bounded L 2 gain performance with respect to matched and unmatched uncertainties in the presence of disturbances. Furthermore, a reaching phase control law is presented to eliminate the undesirable chattering effect and maintain the robustness property all the time whether the system evolves into its sliding mode in finite time or not. Finally, an observer based control law is also developed to achieve the robust performance during the reaching phase. The results are illustrated by an example.