Parametric Control Systems Design - Theory and Applications

Summary form only for tutorial. This paper considers parametric control of high-order descriptor linear systems via proportional plus derivative feedback. It is shown that the problem is closely related with a type of so-called high-order Sylvester matrix equations. By employing general parametric solutions to this type of matrix equations, complete parametric control approaches for high-order linear systems are presented. The proposed approaches give simple complete parametric expressions for the feedback gains and the closed-loop eigenvector matrices, and produce all the design degrees of freedom. Furthermore, an important special case is particular treated and two methods are proposed. The first one utilizes the right factorization of the system, and allows the closed-loop eigenvalues to be set undetermined and sought via certain optimization procedures, the second one mainly depends on a series of singular value decompositions, and is thus numerically simple and reliable. Application directions of the proposed parametric approaches are highlighted.