Parametric stabilization for descriptor linear systems via state-proportional and -derivative feedback. Issue 5 (March 2016)

• Record Type: Journal Article
• Authors: Yu, Hai-Hua
• Is Part Of: Journal of the Franklin Institute. Volume 353:Issue 5(2016:Mar.)
• Page Start: 992
• Page End: 1004
• Publication Date: 2016-03
• Subjects: Science -- Periodicals; Technology -- Periodicals; Patents -- United States -- Periodicals; 505
• DOI: 10.1016/j.jfranklin.2016.01.003
• Languages: English
• ISSNs: 0016-0032

Abstract

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.