Direct design of robustly asymptotically stabilizing hybrid feedback
ESAIM: Control, Optimisation and Calculus of Variations, Tome 15 (2009) no. 1, pp. 205-213.

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.

DOI : 10.1051/cocv:2008023
Classification : 93D15, 49J53, 93B35
Mots-clés : hybrid feedback, nonlinear control system, patchy feedback, robustness, asymptotic stability 
@article{COCV_2009__15_1_205_0,
     author = {Goebel, Rafal and Teel, Andrew R.},
     title = {Direct design of robustly asymptotically stabilizing hybrid feedback},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {205--213},
     publisher = {EDP-Sciences},
     volume = {15},
     number = {1},
     year = {2009},
     doi = {10.1051/cocv:2008023},
     mrnumber = {2488576},
     zbl = {1155.93035},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/cocv:2008023/}
}
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
PY  - 2009
SP  - 205
EP  - 213
VL  - 15
IS  - 1
PB  - EDP-Sciences
UR  - http://www.numdam.org/articles/10.1051/cocv:2008023/
DO  - 10.1051/cocv:2008023
LA  - en
ID  - COCV_2009__15_1_205_0
ER  - 
%0 Journal Article
%A Goebel, Rafal
%A Teel, Andrew R.
%T Direct design of robustly asymptotically stabilizing hybrid feedback
%J ESAIM: Control, Optimisation and Calculus of Variations
%D 2009
%P 205-213
%V 15
%N 1
%I EDP-Sciences
%U http://www.numdam.org/articles/10.1051/cocv:2008023/
%R 10.1051/cocv:2008023
%G en
%F COCV_2009__15_1_205_0
Goebel, Rafal; Teel, Andrew R. Direct design of robustly asymptotically stabilizing hybrid feedback. ESAIM: Control, Optimisation and Calculus of Variations, Tome 15 (2009) no. 1, pp. 205-213. doi : 10.1051/cocv:2008023. http://www.numdam.org/articles/10.1051/cocv:2008023/

[1] F. Ancona and A. Bressan, Patchy vector fields and asymptotic stabilization. ESAIM: COCV 4 (1999) 445-471. | Numdam | MR | Zbl

[2] F. Ancona and A. Bressan, Flow stability of patchy vector fields and robust feedback stabilization. SIAM J. Control Optim. 41 (2003) 1455-1476. | MR | Zbl

[3] F.H. Clarke, Y.S. Ledyaev, E.D. Sontag and A.I. Subbotin, Asymptotic controllability implies feedback stabilization. IEEE Trans. Automat. Control 42 (1997) 1394-1407. | MR | Zbl

[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. | MR | Zbl

[5] R. Goebel and A.R. Teel, Solutions to hybrid inclusions via set and graphical convergence with stability theory applications. Automatica 42 (2006) 573-587. | MR | Zbl

[6] R. Goebel, C. Prieur and A.R. Teel, Smooth patchy control Lyapunov functions, in Proc. 45th IEEE Conference on Decision and Control (2006).

[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 Sciences 281, Springer, Berlin (2003) 285-294. | MR | Zbl

[8] C. Prieur, Asymptotic controllability and robust asymptotic stabilizability. SIAM J. Control Optim. 43 (2005) 1888-1912. | MR | Zbl

[9] C. Prieur, R. Goebel and A.R. Teel, Hybrid feedback control and robust stabilization of nonlinear systems. IEEE Trans. Automat. Control 52 (2007) 2103-2117. | MR

[10] R.T. Rockafellar and R.J.-B. Wets, Variational Analysis. Springer (1998). | MR | Zbl

[11] E.D. Sontag, Clocks and insensitivity to small measurement errors. ESAIM: COCV 4 (1999) 537-557. | Numdam | MR | Zbl

Cité par Sources :