Rafal Goebel


Refereed Journal Submissions

25. Smooth patchy control Lyapunov functions R. Goebel, C. Prieur, and A. Teel; submitted July 2007. Abstract.
24. Relaxation theorems for hybrid inclusions
C. Cai, R. Goebel, and A. Teel; Set-Valued Analysis, to appear. Abstract.
23. The proximal average: basic theory
H. Bauschke, R. Goebel, Y. Lucet, and X. Wang, submitted April 2007. Abstract.
22. Direct design of robustly asymptotically stabilizing hybrid feedback
R. Goebel and A. Teel; ESAIM: Control, Optimisation and Calculus of Variations, to appear. Abstract.
21. Local strong convexity and local Lipschitz continuity of the gradient of convex functions PDF
R. Goebel and R.T. Rockafellar; Journal of Convex Analysis, Volume 15, Number 2, 2008. Abstract.
20. Smooth Lyapunov functions for hybrid systems. Part II: (Pre-)asymptotically stable compact sets
C. Cai, A. Teel, and R. Goebel; IEEE Transactions on Automatic Control, to appear. Abstract.
19. Self-dual smoothing of convex and saddle functions PDF
Rafal Goebel; Journal of Convex Analysis, Volume 15, Number 1, 2008, 179-190, to appear. Abstract.
18. Generalized solutions to hybrid dynamical systems PDF
R. Sanfelice, R. Goebel, and A. Teel; ESAIM: Control, Optimisation and Calculus of Variations, to appear. Abstract.
17. Hybrid feedback control and robust stabilization of nonlinear systems
C. Prieur, R. Goebel, and A. Teel; IEEE Transactions on Automatic Control, Volume 52, Issue 11, 2007, 2103-2117. Abstract.
16. Smooth Lyapunov functions for hybrid systems. Part I: Existence is equivalent to robustness
C. Cai, A. Teel, and R. Goebel; IEEE Transactions on Automatic Control, Volume 52, Issue 7, 2007, 1264-1277. Abstract.
15. Invariance principles for hybrid systems with connections to detectability and asymptotic stability
R. Sanfelice, R. Goebel, and A. Teel; to appear in IEEE Transactions on Automatic Control, Volume 52, Issue 12, 2007, 2282 - 2297. Abstract.
14. Continuous time constrained linear quadratic regulator -- convex duality approach
R. Goebel and M. Subbotin; IEEE Transactions on Automatic Control, Volume 52, Issue 5, 2007, 886-892. Abstract.
13. Conjugate Lyapunov functions for saturated linear systems
T. Hu, R. Goebel, A. Teel, and Z. Lin; Automatica, Volume 41, Issue 11, 2005, 1949-1956. Abstract.
12. Solutions to hybrid inclusions via set and graphical convergence with stability theory applications
R. Goebel and A. Teel; Automatica, Volume 42, Issue 4, 2006, 513-696. Abstract.
11. Conjugate convex Lyapunov functions for dual linear differential inclusions
R. Goebel, A. Teel, T. Hu, and Z. Lin; IEEE Transactions on Automatic Control , Volume 51, Issue 4, 2006, 661-666. Abstract.
10. Stabilizing a linear systems with saturation through optimal control
R. Goebel; IEEE Transactions on Automatic Control , Volume 50, Issue 5, 2005, 650-655. Abstract.
9. Duality and uniqueness of convex solutions to stationary Hamilton-Jacobi equations
R. Goebel; Transactions of AMS, Volume 357, 2005, 2165-2186. Abstract.
8. Convex optimal control problems with smooth Hamiltonians
R. Goebel; SIAM Journal on Control and Optimization, Volume 43, Number 5, 2005, 1787-1811. Abstract.
7. On the nondifferentiability of cone-monotone functions in Banach spaces PDF
J. Borwein and R. Goebel; to appear in Optimization: Structure and Applications, E. Hunt and C.E.M. Pearce editors, Applied Optimization Series, Kluwer Academic Publishers. Abstract.
6. Planar generalized Hamiltonian systems with large saddle sets
R. Goebel; Journal of Nonlinear and Convex Analysis, Volume 3, Number 3, 2002. Abstract.
5. 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, 2004. Abstract.
4. Notions of relative interior in Banach spaces J. Borwein and R. Goebel; Journal of Mathematical Sciences, Volume 115, Issue 4, 2003, 2542-2553. Abstract.
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, 2002 (special issue on Optimiaztion). Abstract.
2. Convexity in zero-sum differential games
R. Goebel; SIAM Journal on Control and Optimization, Vol. 40, Number 5, 2002, 1491-1504. Abstract.
1. Sufficient condition for stability of an L^2-angle
R. Goebel; Bulletin of the Polish Academy of Science, Vol 45, No 3, 1997. Abstract.

Selected Refereed Conference Papers

Linear-convex control and duality PDF
R.T. Rockafellar and R. Goebel; to appear in Proceedings of the Geometric Control and Nonsmooth Analysis Conference, Rome 2006. Abstract.
An introduction to smooth patchy control Lyapunov functions
R. Goebel, C. Prieur and A. Teel; Proceedings of the 45th Conference on Decision and Control, 2006. Abstract.
Results on relaxation theorems for hybrid systems
C. Cai, R. Goebel, and A. Teel; Proceedings of the 45th Conference on Decision and Control, 2006. Abstract.
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. Abstract.
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. Abstract.
Hybrid systems: generalized solutions and robust stability PDF
R. Goebel, J. Hespanha, A. Teel, C. Cai, and R. Sanfelice; NOLCOS 2004. Abstract.
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. Abstract.
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. Abstract.
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. Abstract.

Other contributions

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. Abstract.
Dual matrix inequalities in stability and performance analysis of linear differential/difference inclusions PDF file
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. Abstract.
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. Abstract.
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