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Keywords
(3)
Asymptotic Stability
Control Problem
Feedback Stabilization
Related Publications
(66)
Remarks on continuous feedback
Global asymptotic stabilization for controllable systems without drift
Stability and stabilization: discontinuities and the eect of disturbances
Stabilization by smooth feedback of the angular velocity of a rigid body
Stabilization of a class of nonlinear systems by a smooth feedback control
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ASYMPTOTIC STABILITY AND FEEDBACK STABILIZATION
ASYMPTOTIC STABILITY AND FEEDBACK STABILIZATION,R. W. Brockett
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ASYMPTOTIC STABILITY AND FEEDBACK STABILIZATION
(
Citations: 960
)
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R. W. Brockett
We consider the loca1 behavior of control problems described by (* = dx/dr)
Published in 1982.
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hrl.harvard.edu
)
Citation Context
(598)
...Apart from the fundamental obstruction indicated in Brockett (
1983
) and Zabczyk (
1989
) where the nonexistence of continuous statedependent asymptotic stabilisers was proved, realisation of the control tasks for GNT and nSNT vehicles turns out to be even more problematic...
Maciej Michałek
.
Application of the VFO method to setpoint control for the Ntrailer v...
...According to Brocket’s theorem, a nonholonomic system cannot be stabilized to a goal configuration via continuous and timeinvariant statefeedback [
1
] (i.e., either timevarying and/or discontinuous feedback may provide a solution)...
...Definition 1 [32]: Let F be a collisionfree area for an autonomous vehicle and let (xd ,y d) be the goal position in the interior of F .Am apVh : F → [0,
1
] is a navigation function if it is smooth on F (at least aC 2 function), has a unique...
Augie Widyotriatmo
,
et al.
Navigation FunctionBased Control of Multiple Wheeled Vehicles
...A wellknown result by Brockett [
28
] states that a necessary condition for the existence of a timeinvariant (i.e., not explicitly dependent on time) continuous state feedback law, , that makes asymptotically stable, is that the image of the mapping contains some neighbourhood of . A result by Coron and Rosier [29] states that a control system that can be asymptotically stabilized (in the Filippov sense [29]) by a timeinvariant ...
...Proof: The result by Brockett [
28
] states that the mapping must map an arbitrary neighborhood of onto a neighbourhood of . For this to be true, points of the form must be contained in this mapping for some arbitrary because points of this form are contained in every neighbourhood of . However, these points do not exist for the system in (47) because , , and means that ...
Pål Liljeback
,
et al.
Controllability and Stability Analysis of Planar Snake Robot Locomotio...
...The design of the lower level feedback controllers is more difficult for nonholonomic systems such as wheeled robots, because it is well known that they cannot be stabilized from point to point using a static feedback law and hence, a time varying feedback law has to be used to achieve the stabilization [26], [
27
]...
Suman Chakravorty
,
et al.
Generalized SamplingBased Motion Planners
...Remark 4. It is a classic result [
13
] that, if a system such as (II.2) is nonholonomic, there exists no smooth controller that stabilizes y? asymptotically...
Andrea Censi
,
et al.
Bootstrapping bilinear models of robotic sensorimotor cascades
References
(1)
The structure of the level surfaces of a Lyapunov function
(
Citations: 50
)
Unknown
Published in 1967.
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Citations
(960)
Application of the VFO method to setpoint control for the Ntrailer vehicle with offaxle hitching
Maciej Michałek
Journal:
International Journal of Control  INT J CONTR
, vol. aheadofp, no. aheadofp, pp. 120, 2012
Navigation FunctionBased Control of Multiple Wheeled Vehicles
(
Citations: 5
)
Augie Widyotriatmo
,
KeumShik Hong
Journal:
IEEE Transactions on Industrial Electronics  IEEE TRANS IND ELECTRON
, vol. 58, no. 5, pp. 18961906, 2011
Controllability and Stability Analysis of Planar Snake Robot Locomotion
(
Citations: 4
)
Pål Liljeback
,
Kristin Y. Pettersen
,
Øyvind Stavdahl
,
Jan Tommy Gravdahl
Journal:
IEEE Transactions on Automatic Control  IEEE TRANS AUTOMAT CONTR
, vol. 56, no. 6, pp. 13651380, 2011
Generalized SamplingBased Motion Planners
(
Citations: 2
)
Suman Chakravorty
,
Sandip Kumar
Journal:
IEEE Transactions on Systems, Man, and Cybernetics  TSMC
, vol. 41, no. 3, pp. 855866, 2011
Bootstrapping bilinear models of robotic sensorimotor cascades
(
Citations: 1
)
Andrea Censi
,
Richard M. Murray
Conference:
International Conference on Robotics and Automation  ICRA
, pp. 43184325, 2011