An optimal integral sliding mode control using multiobjective H2/H∞ approach to surface design

In this paper, we propose an optimal method to design the sliding surface in variable structure control (VSC) systems in the presence of matched/mismatched uncertainties and disturbances. A VSC law is designed to guarantee the sliding motion. By solving the problem of optimal surface design with some quadratic constraints, a mixed H
2
/ H
∞
approach is presented to reduce the effect of uncertainties and disturbances on the sliding motion. Solutions to VSC law design problem and surface design problem are based on linear matrix inequalities (LMIs) which can be solved effectively through standard softwares. Finally, using a numerical example, we show the effectiveness of proposed methods.