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