A POINCARE-BENDIXSON THEOREM FOR HYBRID SYSTEMS

被引：4

作者：

Clark, William ^{[1
]}

Bloch, Anthony ^{[1
]}

Colombo, Leonardo ^{[2
]}

机构：

[1] Univ Michigan, Dept Math, 530 Church St, Ann Arbor, MI 48109 USA

[2] Inst Ciencias Math CSIC UAM UC3M UCM, C Nicolas Cabrera 13-15, Madrid 28049, Spain

来源：

MATHEMATICAL CONTROL AND RELATED FIELDS | 2020年 / 10卷 / 01期

关键词：

Poincare-Bendixson theorem; hybrid systems; hybrid flows; stability of periodic orbits; Poincare map; MECHANICAL SYSTEMS; ROBOTS;

D O I：

10.3934/mcrf.2019028

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The Poincare-Bendixson theorem plays an important role in the study of the qualitative behavior of dynamical systems on the plane; it describes the structure of limit sets in such systems. We prove a version of the Poincare-Bendixson Theorem for two dimensional hybrid dynamical systems and describe a method for computing the derivative of the Poincare return map, a useful object for the stability analysis of hybrid systems. We also prove a Poincare-Bendixson Theorem for a class of one dimensional hybrid dynamical systems.

引用

页码：27 / 45

页数：19

共 50 条

[41] POINCARE-BENDIXSON TYPE THEOREMS FOR 2 DIMENSIONAL MANIFOLDS DIFFERENT FROM THE TORUS
HAAS, F
ANNALS OF MATHEMATICS, 1954, 59 (02) : 292 - 299
[42] POINCARE-BENDIXSON THEORY FOR CERTAIN REACTION-DIFFUSION BOUNDARY-VALUE-PROBLEMS
SMITH, RA
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1994, 124 : 33 - 69
[43] DERIVATION AND EVALUATION OF A POINCARE-BENDIXSON THEOREM BASED TARGET ACCELERATION COMPUTATION ALGORITHM FOR AUTONOMOUS DRIVING ON INVERSE TTC AND TIME HEADWAY PLANE
Lee, Hye-Won
Oh, Kwang-Seok
Yoon, Young-Min
Yi, Kyong-Su
PROCEEDINGS OF THE ASME 2020 29TH CONFERENCE ON INFORMATION STORAGE AND PROCESSING SYSTEMS (ISPS2020), 2020,
[44] 关于POINCARE-BENDIXSON环域定理的一个新证明
王成文
山东矿业学院学报, 1990, (03) : 294 - 298
[45] A Poincaré–Bendixson theorem for hybrid dynamical systems on directed graphs
William Clark
Anthony Bloch
Mathematics of Control, Signals, and Systems, 2020, 32 : 1 - 18
[46] Self-Sustaining Oscillations With an Internal Two-Fuzzy Inference System Based on the Poincare-Bendixson Method
Lopez-Renteria, Jorge A.
Herrera-Garcia, Lisdan
Cardenas-Maciel, Selene L.
Aguilar, Luis T.
Cazarez-Castro, Nohe R.
IEEE TRANSACTIONS ON FUZZY SYSTEMS, 2022, 30 (07) : 2563 - 2573
[47] ON A THEOREM OF BENDIXSON
LEFSCHETZ, S
JOURNAL OF DIFFERENTIAL EQUATIONS, 1968, 4 (01) : 66 - +
[48] A generalization of Poincare's theorem to hybrid and impulsive dynamical systems
Nersesov, SG
Chellaboina, V
Haddad, WM
PROCEEDINGS OF THE 2002 AMERICAN CONTROL CONFERENCE, VOLS 1-6, 2002, 1-6 : 1240 - 1245
[49] The Bendixson's theorem and the linear robustness theorem of discontinuous dynamical systems
Sun, JT
Deng, FQ
Liu, YQ
DYNAMICS OF CONTINUOUS DISCRETE AND IMPULSIVE SYSTEMS-SERIES B-APPLICATIONS & ALGORITHMS, 2003, : 362 - 365
[50] ON POINCARE BENDIXSON THEOREM AND NON-TRIVIAL MINIMAL SETS IN PLANAR NONSMOOTH VECTOR FIELDS
Buzzi, Claudio A.
Carvalho, Tiago
Euzebio, Rodrigo D.
PUBLICACIONS MATEMATIQUES, 2018, 62 (01) : 113 - 131

← 1 2 3 4 5 →