Rest point theorems for autonomous control systems

M.L.J. Hautus; M. Heymann; R.J. Stern

doi:10.1016/0022-247X(77)90231-1

Rest point theorems for autonomous control systems

M.L.J. Hautus, M. Heymann, R.J. Stern

Center for Analysis, Scientific Computing and Applications

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

2 Citations (Scopus)

Abstract

The classical Poincaré-Bendixson theory in the plane is generalized to multivalued vector fields. For control systems where the state x is in Rn and the control u is valued in a compact subset of Rm we study the existence (and nonexistence) of rest states. Some special emphasis is focused on the case n = 2.

Original language	English
Pages (from-to)	98-112
Number of pages	15
Journal	Journal of Mathematical Analysis and Applications
Volume	58
Issue number	1
DOIs	https://doi.org/10.1016/0022-247X(77)90231-1
Publication status	Published - 1977

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10.1016/0022-247X(77)90231-1

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title = "Rest point theorems for autonomous control systems",

abstract = "The classical Poincar{\'e}-Bendixson theory in the plane is generalized to multivalued vector fields. For control systems where the state x is in Rn and the control u is valued in a compact subset of Rm we study the existence (and nonexistence) of rest states. Some special emphasis is focused on the case n = 2.",

author = "M.L.J. Hautus and M. Heymann and R.J. Stern",

year = "1977",

doi = "10.1016/0022-247X(77)90231-1",

language = "English",

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pages = "98--112",

journal = "Journal of Mathematical Analysis and Applications",

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T1 - Rest point theorems for autonomous control systems

AU - Hautus, M.L.J.

AU - Heymann, M.

AU - Stern, R.J.

PY - 1977

Y1 - 1977

N2 - The classical Poincaré-Bendixson theory in the plane is generalized to multivalued vector fields. For control systems where the state x is in Rn and the control u is valued in a compact subset of Rm we study the existence (and nonexistence) of rest states. Some special emphasis is focused on the case n = 2.

AB - The classical Poincaré-Bendixson theory in the plane is generalized to multivalued vector fields. For control systems where the state x is in Rn and the control u is valued in a compact subset of Rm we study the existence (and nonexistence) of rest states. Some special emphasis is focused on the case n = 2.

U2 - 10.1016/0022-247X(77)90231-1

DO - 10.1016/0022-247X(77)90231-1

M3 - Article

SN - 0022-247X

VL - 58

SP - 98

EP - 112

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

ER -

Rest point theorems for autonomous control systems

Abstract

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