Parametric stabilization for descriptor linear systems via state-proportional and -derivative feedback. Issue 5 (March 2016) - Yu, Hai-Hua
Abstract: This paper considers eigenstructure assignment problem for descriptor linear systems via state-proportional and -derivative feedback. New complete parametric approaches for the problem are proposed in two cases. General complete parametric expressions in direct closed forms for the closed-loop eigenvectors associated with the finite closed-loop eigenvalues are presented. Based on a recently proposed complete parametric solution to the generalized Sylvester matrix equation AV − EVJ = BW D J + BW P, very simple complete parametric solutions to the feedback gains are also established. The approach guarantees arbitrary assignment of rank [ E B ] number finite closed-loop eigenvalues with arbitrary given algebraic and geometric multiplicities. It also guarantees the closed-loop regularity and impulse-freeness when several simple constraints on the design parameters are added. A numerical example shows the effectiveness of the proposed approaches.