Robust Sliding Mode Control Design for Mismatched Uncertain Systems with a Gℋ2/ℋ∞ Performance

This paper presents an optimal design of sliding mode controller with a Gℋ2/ℋ∞ constraint for a general class of uncertain systems. The method proposed here takes into account nonmatching disturbance signals and nonmatching system model uncertainties. Without requiring any transformation or restriction on the input matrix, our approach leads to a straightforward design which can be easily solved by using linear matrix inequality (LMI) technique. By solving the problem of optimal sliding motion design with some quadratic constraints based on LMIs, a mixed Gℋ2/ℋ∞ approach is presented to reduce the effect of uncertainties and disturbances on the sliding motion. Finally, we give simulation results for controlling a chemical reactor to illustrate the applicability of the proposed scheme for uncertain time‐delay systems or mismatched uncertain systems.