Sliding mode methodology and LMIs based controller design for performance enhancement and chattering reduction

Based on the main concept of sliding mode control (SMC) theory, this study proposes a robust control law for a class of multivariable linear uncertain systems. As in conventional SMC, the developed method provides robustness against to matched model uncertainty and unknown external disturbances. A control gain used for system transformation is obtained by incorporating linear matrix inequalities (LMIs) such that the resulting reduced order dynamics is robust stable in the face of unmatched model uncertainty. In addition, the LMIs are further refined to achieve better performance and smaller control effort. Moreover, a continuous controller is finally designed for chattering elimination. Building on the synthetic control framework, all the controlled system trajectories are ultimately bounded by a disc, where the radius decreases as time increases and therefore arbitrary control precision is achieved.