A note on Poisson stability and controllability

作者：Wang Xiaoming^*; Cui Pingyuan; Cui Hutao

来源：Nonlinear Dynamics, 2011, 66(4): 789-793.

DOI：10.1007/s11071-011-9951-3

• Poisson stability
• Controllability
• Vector field
• Lie algebra
• Riemannian manifold

The connection between Poisson stability and controllability is revisited. For the controllability criterion based on weakly positive Poisson stability (WPPS) and Lie algebra rank condition (LARC), it is shown that two natural assumptions about the set of input values are necessary for strictness. By using the relationship between conservative property and WPPS, sufficient conditions for controllability of affine nonlinear systems are further discussed. At last, for systems defined on compact Riemannian manifold, the WPPS is proved to be equivalent to Poisson stability.

• 出版日期2011-12
• 单位哈尔滨工业大学