Infinite eigenvalue assignment in linear time-invariant descriptor systems via proportional plus derivative state feedback

Author

Xian Zhang ; Yuqiu Sheng ; Chong Tan

Author_Institution

Center for Control Theor. & Guidance Technol., Harbin Inst. of Technol., Harbin

fYear

2008

fDate

16-18 July 2008

Firstpage

782

Lastpage

786

Abstract

A parametric approach, based on a canonical form of the singular matrix pencils and a result about the regularizability of linear descriptor systems, is proposed for infinite eigenvalue assignment (IEVA) in linear, continuous and time-invariant descriptor systems via proportional plus derivative state feedback. When the input and state vectors have the same dimension, it is proved that there are solutions to the IEVA problem. A representation of all these solutions is given. When the input and state vectors have different dimensions, necessary and sufficient conditions under which the IEVA problem has at least a solution are presented and a parametric expression of a class of all solutions is given. A design algorithm and two test examples show the efficiency of the proposed approach.

Keywords

PD control; continuous systems; eigenvalues and eigenfunctions; invariance; linear systems; state feedback; continuous system; infinite eigenvalue assignment; linear time-invariant descriptor system; proportional plus derivative state feedback; singular matrix pencils; state vector; Control systems; Control theory; Eigenvalues and eigenfunctions; Linear feedback control systems; Matrix decomposition; PD control; Proportional control; State feedback; Sufficient conditions; Vectors; Infinite eigenvalue; Linear descriptor systems; Proportional plus derivative state feedback;

fLanguage

English

Publisher

ieee

Conference_Titel

Control Conference, 2008. CCC 2008. 27th Chinese

Conference_Location

Kunming

Print_ISBN

978-7-900719-70-6

Electronic_ISBN

978-7-900719-70-6

Type

conf

DOI

10.1109/CHICC.2008.4605898

Filename

4605898