Rafal Goebel
Books
Hybrid Dynamical Systems: Modeling, Stability, and Robustness
Rafal Goebel, Ricardo G. Sanfelice, and Andrew R. Teel, Princeton
University Press, 2012.
Refereed Journal Submissions
35. Robustness of Stability through Necessary and Sufficient
Lyapunov-like Conditions for Systems with a Continuum of
Equilibria PDF
R. Goebel, submitted June 2013.
34. Lyapunov functions and duality for convex processes PDF
R. Goebel, SIAM
Journal on Control and Optimization, Volume 51, Issue 4,
3332-3350, 2013.
33. Quasiconvex functions and nonlinear PDEs
E.N.Barron, R. Goebel, and R.R. Jensen, Transactions
of the AMS, Volume 365, 4229-4255, 2013.
32. Functions which are quasiconvex under linear
perturbations
E.N.Barron, R. Goebel, and R.R. Jensen, SIAM
Journal on Optimization, Volume 22, Issue 3, 1089-1108,
2012.
31. The quasiconvex envelope through first-order partial
differential equations which characterize quasiconvexity of
nonsmooth functions
E.N.Barron, R. Goebel, and R.R. Jensen, Discrete
and Continuous Dynamical Systems - Series B, Volume 17,
Issue 6, 1693-1706, 2012.
30. The optimal value and optimal solutions of the
proximal average of convex functions
Rafal Goebel, W. Hare, and X. Wang, Nonlinear
Analysis: Theory, Methods & Applications, Volume 75,
Issue 3, 1290-1304, 2012.
29. Set-valued Lyapunov functions for difference
inclusions PDF
R. Goebel, Automatica,Volume
47, Issue 1, 127-132, 2011.
28. The proximal average for saddle functions and its
symmetry properties with respect to partial and saddle conjugacy
PDF
R. Goebel, Journal of
Nonlinear and Convex Analysis, Volume 11, Number 1, 1-11,
2010.
27. Best response dynamics for continuous games
E.N. Barron, R. Goebel, and R.R. Jensen, Proceedings of the AMS,
Volume 138, Number 3, 1069-1083, 2010.
26. Pre-asymptotic stability and homogeneous approximation
of hybrid dynamical systems PDF
R. Goebel and A.R. Teel; SIAM Review,
Volume 52, Number 1, 87-109, 2010.
25. Smooth patchy control Lyapunov functions PDF
R. Goebel, C. Prieur, and A. Teel; Automatica,
Volume 45, 675-683, 2009.
24. Direct design of robustly asymptotically stabilizing
hybrid feedback PDF
R. Goebel and A. Teel; ESAIM: Control, Optimisation and Calculus
of Variations, Volume 15, Number 1, 205-213, 2009.
The original publication is available at www.esaim-cocv.org.
23. Relaxation theorems for hybrid inclusions
C. Cai, R. Goebel, and A. Teel; Set-Valued
Analysis, Volume 16, Issue 5, 2008, 733-757.
22. Invariance principles for switching systems via hybrid
systems techniques PDF
R. Goebel, R. Sanfelice, and A. Teel; Systems
& Control Letters, Volume 57, 980-986, 2008.
21. Generalized solutions to hybrid dynamical systems PDF
R. Sanfelice, R. Goebel, and A. Teel; ESAIM: Control, Optimisation
and Calculus of Variations, Volume 14, 699-724, 2008.
The original publication is available at www.esaim-cocv.org.
20. The proximal average: basic theory PDF
H. Bauschke, R. Goebel, Y. Lucet, and X. Wang; SIAM Journal on
Optimization, Volume 19, Number 2, 766-785, 2008.
19. Local strong convexity and local Lipschitz continuity
of the gradient of convex functions
R. Goebel and R.T. Rockafellar; Journal of
Convex Analysis, Volume 15, Number 2, 263-270, 2008.
18. Self-dual smoothing of convex and saddle functions
R. Goebel; Journal
of Convex Analysis, Volume 15, Number 1, 179-190, 2008.
17. Smooth Lyapunov functions for hybrid systems. Part II:
(Pre-)asymptotically stable compact sets PDF
C. Cai, A. Teel, and R. Goebel; IEEE Transactions on
Automatic Control, Volume 53, Number 3, 734-748, 2008.
16. Invariance principles for hybrid systems with
connections to detectability and asymptotic stability PDF
R. Sanfelice, R. Goebel, and A. Teel; to appear in IEEE Transactions on
Automatic Control, Volume 52, Issue 12, 2282-2297, 2007.
15. Hybrid feedback control and robust stabilization of
nonlinear systems PDF
C. Prieur, R. Goebel, and A. Teel; IEEE Transactions on
Automatic Control, Volume 52, Issue 11, 2103-2117, 2007.
14. Smooth Lyapunov functions for hybrid systems. Part I:
Existence is equivalent to robustness PDF
C. Cai, A. Teel, and R. Goebel; IEEE Transactions on
Automatic Control, Volume 52, Issue 7, 1264-1277, 2007.
13. Continuous time constrained linear quadratic regulator
- convex duality approach PDF
R. Goebel and M. Subbotin; IEEE
Transactions
on Automatic Control, Volume 52, Issue 5, 886-892, 2007.
12. Conjugate convex Lyapunov functions for dual linear
differential inclusions PDF
R. Goebel, A. Teel, T. Hu, and Z. Lin; IEEE Transactions on
Automatic Control , Volume 51, Issue 4, 661-666, 2006.
11. Solutions to hybrid inclusions via set and graphical
convergence with stability theory applications PDF
R. Goebel and A. Teel; Automatica,
Volume 42, Issue 4, 513-696, 2006.
10. Conjugate Lyapunov functions for saturated linear
systems
T. Hu, R. Goebel, A. Teel, and Z. Lin; Automatica,
Volume 41, Issue 11, 1949-1956, 2005.
9. Stabilizing a linear systems with saturation through
optimal control PDF
R. Goebel; IEEE
Transactions on Automatic Control , Volume 50, Issue 5,
650-655, 2005.
8. Duality and uniqueness of convex solutions to stationary
Hamilton-Jacobi equations
R. Goebel; Transactions
of AMS, Volume 357, 2165-2186, 2005.
7. Convex optimal control problems with smooth Hamiltonians
PDF
R. Goebel; SIAM
Journal on Control and Optimization, Volume 43, Number 5,
1787-1811, 2005.
6. Regularity of the optimal feedback and the value
function in convex problems of optimal control
R. Goebel; Set-Valued
Analysis, Volume 12, Issue 1-2, 127-145, 2004.
5. Notions of relative interior in Banach spaces
J. Borwein and R. Goebel; Journal of
Mathematical Sciences, Volume 115, Issue 4, 2542-2553, 2003.
4. Planar generalized Hamiltonian systems with large saddle
sets
R. Goebel;
Journal of Nonlinear and Convex Analysis, Volume 3, Number
3, 365-380, 2002.
3. Generalized conjugacy in Hamilton-Jacobi theory for
fully convex Lagrangians
R. Goebel and R. T. Rockafellar; Journal of
Convex Analysis, Volume 9, Number 2, 463-473, 2002.
2. Convexity in zero-sum differential games
R. Goebel; SIAM
Journal on Control and Optimization, Vol. 40, Number 5,
1491-1504, 2002.
1. Sufficient condition for stability of an L^2-angle
R. Goebel; Bulletin of the Polish Academy of Science, Vol 45, No
3, 227-232, 1997.
Selected Refereed Conference Papers
Zeno behavior in homogeneous hybrid systems
R. Goebel and A. Teel; Proceedings of the 47th Conference on
Decision and Control, 2008.
Lyapunov characterization of Zeno behavior in hybrid
systems
R. Goebel and A. Teel; Proceedings of the 47th Conference on
Decision and Control, 2008.
Linear-convex control and duality PDF
R.T. Rockafellar and R. Goebel; Proceedings of the Geometric
Control and Nonsmooth Analysis Conference, Rome 2006.
On the robustness to measurement noise and unmodeled
dynamics of stability in hybrid systems
R. Sanfelice, A. Teel, and C. Prieur, Proceedings of the 2006
American Control Conference, 2006, 4061 - 4066.
Dissipativity for dual linear differential inclusions
through conjugate storage functions PDF
R.Goebel, A. Teel, T. Hu, and Z. Lin; Proceedings of the 43nd IEEE
Conference on Decision and Control, 2004.
Hybrid systems: generalized solutions and robust stability
PDF
R. Goebel, J. Hespanha, A. Teel, C. Cai, and R. Sanfelice; NOLCOS 2004.
A factorization approach to C^1 stabilization of nonlinear
triangular systems PDF
D. Dacic, R. Goebel, and P. Kokotovic; Proceedings of the 42nd
IEEE Conference on Decision and Control, 2003.
Stationary Hamilton-Jacobi equations for convex control
problems - uniqueness and duality of solutions
R. Goebel; M. de Queiroz, M. Malisoff, and P. Wolenski, Editors, Optimal
Control, Stabilization, and Nonsmooth Analysis, Lecture
Notes in Control and Information Sciences, Springer-Verlag,
Heidelberg, 2004.
Hamiltonian dynamical systems for convex problems of
optimal control: implications for the value function PDF
Proceedings of the 41st IEEE Conference on Decision and Control,
Volume 1, 2002, 728-732.
Other contributions
On the nondifferentiability of cone-monotone functions in
Banach spaces
J. Borwein and R. Goebel Optimization: Structure and Applications,
E. Hunt and C. Pearce editors, Optimization and Its Applications,
Volume 32, 3-14, Springer, 2009.
Hybrid dynamical systems. Robust stability and control for
systems that combine continuous-time and discrete-time dynamics,
R. Goebel, R. Sanfelice, and A.R. Teel, IEEE Control Systems
Magazine, Volume 29, Issue 2, 2009, 28-93.
Hybrid control systems
A.R. Teel, R. Sanfelice, and R. Goebel, Encyclopedia of Complexity
and Systems Science, R.A. Meyers, Editor, Springer, 2009.
Hybrid systems: limit sets and zero dynamics with a view
toward output regulation
C. Cai, R. Goebel, R.G. Sanfelice, and A.R. Teel; Analysis and
Design of Nonlinear Control Systems. In Honor of Alberto Isidori,
237-257, Springer-Verlag, 2007.
Dual matrix inequalities in stability and performance
analysis of linear differential/difference inclusions PDF
R. Goebel, T. Hu, and A.R. Teel; Current trends in nonlinear
systems and control, 103-122, Systems Control Found. Appl.,
Birkhäuser Boston, Boston, MA, 2006.
Convexity, Convergence and Feedback in Optimal Control
R. Goebel; Doctoral Dissertation, Department of Mathematics,
University of Washington, 2000.
Convexity and Hamiltonian equations in differential games
R. Goebel; Interim Report, International
Institute of Applied Systems Analysis, August 98.
On the Stability of an $L^2-$angle
R. Goebel; Masters Thesis (in Polish), Department of Mathematics,
University of Maria Curie-Sklodowska, Lublin, Poland, 1994.
AMS
Reviews