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Direct design of robustly asymptotically stabilizing hybrid feedback

Published online by Cambridge University Press:  23 January 2009

Rafal Goebel
Affiliation:
Research carried out at the Center for Control, Dynamical Systems, and Computation; Department of Electrical and Computer Engineering; University of California, Santa Barbara.Current address: 3518 NE 42 St., Seattle, WA 98105, USA. rafal.k.goebel@gmail.com.
Andrew R. Teel
Affiliation:
Center for Control, Dynamical Systems, and Computation; Department of Electrical and Computer Engineering; University of California, Santa Barbara, CA 93106-9560, USA. teel@ece.ucsb.edu.
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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.

Type
Research Article
Copyright
© EDP Sciences, SMAI, 2008

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References

Ancona, F. and Bressan, A., Patchy vector fields and asymptotic stabilization. ESAIM: COCV 4 (1999) 445471. CrossRef
Ancona, F. and Bressan, A., Flow stability of patchy vector fields and robust feedback stabilization. SIAM J. Control Optim. 41 (2003) 14551476. CrossRef
Clarke, F.H., Ledyaev, Y.S., Sontag, E.D. and Subbotin, A.I., Asymptotic controllability implies feedback stabilization. IEEE Trans. Automat. Control 42 (1997) 13941407. CrossRef
Clarke, F.H., Ledyaev, Y.S., Rifford, L. and Stern, R.J., Feedback stabilization and Lyapunov functions. SIAM J. Control Optim. 39 (2000) 2548. CrossRef
Goebel, R. and Teel, A.R., Solutions to hybrid inclusions via set and graphical convergence with stability theory applications. Automatica 42 (2006) 573587. CrossRef
R. Goebel, C. Prieur and A.R. Teel, Smooth patchy control Lyapunov functions, in Proc. 45th IEEE Conference on Decision and Control (2006).
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.
Prieur, C., Asymptotic controllability and robust asymptotic stabilizability. SIAM J. Control Optim. 43 (2005) 18881912. CrossRef
Prieur, C., Goebel, R. and Teel, A.R., Hybrid feedback control and robust stabilization of nonlinear systems. IEEE Trans. Automat. Control 52 (2007) 21032117. CrossRef
R.T. Rockafellar and R.J.-B. Wets, Variational Analysis. Springer (1998).
Sontag, E.D., Clocks and insensitivity to small measurement errors. ESAIM: COCV 4 (1999) 537557. CrossRef

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