A note on Poisson stability and controllability

Xiaoming Wang; Pingyuan Cui; Hutao Cui

doi:10.1007/s11071-011-9951-3

A note on Poisson stability and controllability

Xiaoming Wang^*, Pingyuan Cui, Hutao Cui

^*Corresponding author for this work

Harbin Institute of Technology

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	789-793
Number of pages	5
Journal	Nonlinear Dynamics
Volume	66
Issue number	4
DOIs	https://doi.org/10.1007/s11071-011-9951-3
Publication status	Published - Dec 2011
Externally published	Yes

Keywords

Controllability
Lie algebra
Poisson stability
Riemannian manifold
Vector field

Access to Document

10.1007/s11071-011-9951-3

Cite this

Wang, X., Cui, P., & Cui, H. (2011). A note on Poisson stability and controllability. Nonlinear Dynamics, 66(4), 789-793. https://doi.org/10.1007/s11071-011-9951-3

@article{77895ad101664a7180be054f05cfc99a,

title = "A note on Poisson stability and controllability",

abstract = "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.",

keywords = "Controllability, Lie algebra, Poisson stability, Riemannian manifold, Vector field",

author = "Xiaoming Wang and Pingyuan Cui and Hutao Cui",

year = "2011",

month = dec,

doi = "10.1007/s11071-011-9951-3",

language = "English",

volume = "66",

pages = "789--793",

journal = "Nonlinear Dynamics",

issn = "0924-090X",

publisher = "Springer Netherlands",

number = "4",

}

TY - JOUR

T1 - A note on Poisson stability and controllability

AU - Wang, Xiaoming

AU - Cui, Pingyuan

AU - Cui, Hutao

PY - 2011/12

Y1 - 2011/12

N2 - 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.

AB - 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.

KW - Controllability

KW - Lie algebra

KW - Poisson stability

KW - Riemannian manifold

KW - Vector field

UR - http://www.scopus.com/inward/record.url?scp=82255164102&partnerID=8YFLogxK

U2 - 10.1007/s11071-011-9951-3

DO - 10.1007/s11071-011-9951-3

M3 - Article

AN - SCOPUS:82255164102

SN - 0924-090X

VL - 66

SP - 789

EP - 793

JO - Nonlinear Dynamics

JF - Nonlinear Dynamics

IS - 4

ER -

A note on Poisson stability and controllability

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this