Title :
Linear symmetry of nonlinear systems
Author :
Cheng, Diazhan ; Yang, Guowu
Author_Institution :
Inst. of Syst. Sci., Acad. Sinica, Beijing, China
Abstract :
This paper tackles the symmetries of control systems. Main attention has been focused on the linear symmetry of affine nonlinear systems. That is, the symmetry under the action of a sub-group of general linear group GL(n,R). The structure of the groups of symmetry and their Lie algebras is investigated. Using left semi-tensor product, a complete classification of symmetric plane systems is presented. Finally, a set of linear algebraic equations are presented, whose solutions provide the largest Lie algebra. Its connected Lie group is the largest one, with which the system is symmetric
Keywords :
Lie algebras; group theory; linear algebra; nonlinear control systems; symmetry; Lie algebras; general linear group; left semitensor product; linear algebraic equations; linear symmetry; nonlinear systems; subgroup; symmetric plane system classification; Algebra; Control systems; Nonlinear equations; Nonlinear systems; Polynomials; State-space methods; Taylor series; Tensile stress; Zinc;
Conference_Titel :
Decision and Control, 2001. Proceedings of the 40th IEEE Conference on
Conference_Location :
Orlando, FL
Print_ISBN :
0-7803-7061-9
DOI :
10.1109/.2001.981164
