Sliding surface design for discrete VSS using LQR technique with a preset real eigenvalue

Abstract This paper presents an LQR-based sliding surface design procedure that allows one to specify a desired weighting matrix and a desired real eigenvalue which is important in discrete VSS. The procedure computes a weighting matrix that simultaneously stays “closest” to the desired one and yields the desired eigenvalue. Sliding surface is then determined from the LQR gain matrix and the desired eigenvalue. It is shown that feasible weighting matrices almost always exist and are not unique. Moreover, the underlying constrained optimization problem is convex and least-squares method may be used to simplify or solve the problem. The paper ends with two numerical examples that illustrate the design procedure.