Robust sliding hyperplane design for parametric uncertain systems by Riccati approach

We propose a novel method to design a robust sliding hyperplane in the presence of parametric uncertainty, which may be mismatched, based on the quadratic stability with scalings. The robust sliding hyperplane on which the sliding motion is quadratically stable is constructed from the Riccati solution matrix which solves the quadratic stabilizability via static linear full state feedback in the absence of external disturbances. The proposed method is effective in that it does not require the canonical transformation and enables one to optimize the sliding motion by applying the robust H₂ control idea