Stabilization of linear systems constrained by algebraic equations

Author

Shafai, B. ; Oloomi, H.

Author_Institution

Dept. of Electr. & Comput. Eng., Northeastern Univ., Boston, MA, USA

Volume

3

fYear

1997

fDate

4-6 Jun 1997

Firstpage

2063

Abstract

We study the stabilization problem of linear systems with state algebraic-equation constraint. We show that this problem reduces to a constrained stabilization problem, which requires the stability of the closed-loop system and simultaneous satisfaction of a pure matrix algebraic equation in terms of the feedback gain. We provide a necessary and sufficient condition for the existence of the solution to this new constrained stabilization problem and outline a simple method for its solution. The condition for the existence of a controller with complete eigenvalue assignability is also discussed. Finally, the problem of observer for linear systems with algebraic equation constraint is formulated and solved

Keywords

asymptotic stability; closed loop systems; eigenvalues and eigenfunctions; feedback; linear systems; matrix algebra; observers; closed-loop system; complete eigenvalue assignability; constrained stabilization problem; feedback gain; linear systems; necessary and sufficient condition; observer; pure matrix algebraic equation; state algebraic-equation constraint; Control systems; Controllability; Eigenvalues and eigenfunctions; Equations; Feedback loop; Lagrangian functions; Linear systems; Observability; Stability; Sufficient conditions;

fLanguage

English

Publisher

ieee

Conference_Titel

American Control Conference, 1997. Proceedings of the 1997

Conference_Location

Albuquerque, NM

ISSN

0743-1619

Print_ISBN

0-7803-3832-4

Type

conf

DOI

10.1109/ACC.1997.611053

Filename

611053