Hyperplane design for sliding mode control of sampled systems based on the discrete-time Riccati equation

For sliding mode control, the specification of switching hyperplane is very important because the steady state system performance depends on it. The fundamental requirement on choosing the hyperplane matrix is previously based on certain properties of some matrices in terms of invertibility and stability, which is not intuitive. In solving this problem, the Riccati equation and the stabilizability assumption have been utilized in some studies. However, the inter-relations among these factors have not been clearly explained. This paper is devoted to clarifying this issue.