Solving Lyapunov equations symbolically

Author

Abdalla, M. ; Wang, R. ; McLauchlan, R.

Author_Institution

Texas A&M Univ., Kingsville, TX, USA

fYear

1996

Firstpage

504

Lastpage

509

Abstract

Symbolic manipulation is an indispensable tool in control design and in system analysis. While numeric computational languages and algorithms have been exhaustively used, symbolic manipulation methods have been barely used at all. In this study, we developed a Maple language procedure to solve continuous Lapunov equations symbolically in conjunction with the Kronecker product. A Lyapunov continuous algebraic equation of the form A^TP+PA+Q=0 was considered. The method is also applicable to time-variant and non-constant systems. Examples were incorporated to test the method over different order systems and results were compared with the published solutions of Gonzalez and Munro (1990, 1991). A thorough study of the system stability of a non-constant system matrix A is also introduced and analyzed. Maple source code procedures are presented and fully commented on

Keywords

Lyapunov matrix equations; control system CAD; control system analysis computing; mathematics computing; stability; symbol manipulation; Kronecker product; Lyapunov continuous algebraic equation; Maple language procedure; Maple source code procedures; control design; control system analysis; nonconstant system matrix; symbolic manipulation; system stability; time-variant systems; Continuous time systems; Differential algebraic equations; Differential equations; Eigenvalues and eigenfunctions; Packaging; Software packages; Stability analysis; Symmetric matrices; System testing; Time varying systems;

fLanguage

English

Publisher

ieee

Conference_Titel

Computer-Aided Control System Design, 1996., Proceedings of the 1996 IEEE International Symposium on

Conference_Location

Dearborn, MI

Print_ISBN

0-7803-3032-3

Type

conf

DOI

10.1109/CACSD.1996.555344

Filename

555344