Direct design of robustly asymptotically stabilizing hybrid feedback

Rafal Goebel; Andrew R. Teel

ESAIM: Control, Optimisation and Calculus of Variations (2009)

  • Volume: 15, Issue: 1, page 205-213
  • ISSN: 1292-8119

Abstract

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A direct construction of a stabilizing hybrid feedback that is robust to general measurement error is given for a general nonlinear control system that is asymptotically controllable to a compact set.

How to cite

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Goebel, Rafal, and Teel, Andrew R.. "Direct design of robustly asymptotically stabilizing hybrid feedback." ESAIM: Control, Optimisation and Calculus of Variations 15.1 (2009): 205-213. <http://eudml.org/doc/250564>.

@article{Goebel2009,
abstract = { A direct construction of a stabilizing hybrid feedback that is robust to general measurement error is given for a general nonlinear control system that is asymptotically controllable to a compact set. },
author = {Goebel, Rafal, Teel, Andrew R.},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Hybrid feedback; nonlinear control system; patchy feedback; robustness; asymptotic stability; hybrid feedback; asymptotic stability},
language = {eng},
month = {1},
number = {1},
pages = {205-213},
publisher = {EDP Sciences},
title = {Direct design of robustly asymptotically stabilizing hybrid feedback},
url = {http://eudml.org/doc/250564},
volume = {15},
year = {2009},
}

TY - JOUR
AU - Goebel, Rafal
AU - Teel, Andrew R.
TI - Direct design of robustly asymptotically stabilizing hybrid feedback
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2009/1//
PB - EDP Sciences
VL - 15
IS - 1
SP - 205
EP - 213
AB - A direct construction of a stabilizing hybrid feedback that is robust to general measurement error is given for a general nonlinear control system that is asymptotically controllable to a compact set.
LA - eng
KW - Hybrid feedback; nonlinear control system; patchy feedback; robustness; asymptotic stability; hybrid feedback; asymptotic stability
UR - http://eudml.org/doc/250564
ER -

References

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  1. F. Ancona and A. Bressan, Patchy vector fields and asymptotic stabilization. ESAIM: COCV4 (1999) 445–471.  Zbl0924.34058
  2. F. Ancona and A. Bressan, Flow stability of patchy vector fields and robust feedback stabilization. SIAM J. Control Optim.41 (2003) 1455–1476.  Zbl1055.34094
  3. F.H. Clarke, Y.S. Ledyaev, E.D. Sontag and A.I. Subbotin, Asymptotic controllability implies feedback stabilization. IEEE Trans. Automat. Control42 (1997) 1394–1407.  Zbl0892.93053
  4. F.H. Clarke, Y.S. Ledyaev, L. Rifford and R.J. Stern, Feedback stabilization and Lyapunov functions. SIAM J. Control Optim.39 (2000) 25–48.  Zbl0961.93047
  5. R. Goebel and A.R. Teel, Solutions to hybrid inclusions via set and graphical convergence with stability theory applications. Automatica42 (2006) 573–587.  Zbl1106.93042
  6. R. Goebel, C. Prieur and A.R. Teel, Smooth patchy control Lyapunov functions, in Proc. 45th IEEE Conference on Decision and Control (2006).  Zbl1166.93022
  7. C. Prieur, Perturbed hybrid systems, applications in control theory, in Nonlinear and adaptive control, A. Zinober and D. Owens Eds., Lecture Notes in Control and Information Sciences281, Springer, Berlin (2003) 285–294.  Zbl1010.93088
  8. C. Prieur, Asymptotic controllability and robust asymptotic stabilizability. SIAM J. Control Optim.43 (2005) 1888–1912.  Zbl1116.93023
  9. C. Prieur, R. Goebel and A.R. Teel, Hybrid feedback control and robust stabilization of nonlinear systems. IEEE Trans. Automat. Control52 (2007) 2103–2117.  
  10. R.T. Rockafellar and R.J.-B. Wets, Variational Analysis. Springer (1998).  
  11. E.D. Sontag, Clocks and insensitivity to small measurement errors. ESAIM: COCV4 (1999) 537–557.  Zbl0984.93068

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