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.
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://archive.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://archive.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://archive.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://archive.numdam.org/articles/10.1051/cocv:2008023/
[1] Patchy vector fields and asymptotic stabilization. ESAIM: COCV 4 (1999) 445-471. | Numdam | MR | Zbl
and ,[2] Flow stability of patchy vector fields and robust feedback stabilization. SIAM J. Control Optim. 41 (2003) 1455-1476. | MR | Zbl
and ,[3] Asymptotic controllability implies feedback stabilization. IEEE Trans. Automat. Control 42 (1997) 1394-1407. | MR | Zbl
, , and ,[4] Feedback stabilization and Lyapunov functions. SIAM J. Control Optim. 39 (2000) 25-48. | MR | Zbl
, , and ,[5] Solutions to hybrid inclusions via set and graphical convergence with stability theory applications. Automatica 42 (2006) 573-587. | MR | Zbl
and ,[6] Smooth patchy control Lyapunov functions, in Proc. 45th IEEE Conference on Decision and Control (2006).
, and ,[7] 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] Asymptotic controllability and robust asymptotic stabilizability. SIAM J. Control Optim. 43 (2005) 1888-1912. | MR | Zbl
,[9] Hybrid feedback control and robust stabilization of nonlinear systems. IEEE Trans. Automat. Control 52 (2007) 2103-2117. | MR
, and ,[10] Variational Analysis. Springer (1998). | MR | Zbl
and ,[11] Clocks and insensitivity to small measurement errors. ESAIM: COCV 4 (1999) 537-557. | Numdam | MR | Zbl
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