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引用
期刊论文
Nonlinear systems possessing linear symmetry
INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL Int. J. Robust Nonlinear Control 2007; 17: 51-81,-0001,():
This paper tackles linear symmetries of control systems. Precisely, the symmetry of affine nonlinear systems under the action of a sub-group of general linear group GL?n;R?: First of all, the structure of state space (briefly, ss) symmetry group and its Lie algebra for a given system is investigated. Secondly, the structure of systems, which are ss-symmetric under rotations, is revealed. Thirdly, a complete classification of ss-symmetric planar systems is presented. It is shown that for planar systems there are only four classes of systems which are ss-symmetric with respect to four linear groups. Fourthly, a set of algebraic equations are presented, whose solutions provide the Lie algebra of the largest connected ss-symmetry group. Finally, some controllability properties of systems with ss-symmetry group are studied. As an auxiliary tool for computation, the concept and some properties of semi-tensor product of matrices are included. Copyright
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