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Stabilization via symmetry switching in hybrid dynamical systems
1. | Chair of Applied Mathematics, University of Paderborn, D-33098 Paderborn, Germany, Germany |
References:
[1] |
M. Dellnitz and S. Hage-Packhäuser, A global symmetry framework for Hybrid dynamical systems,, preprint., ().
|
[2] |
B. Dionne, M. Golubitsky and I. Stewart, Coupled cells with internal symmetry: I. Wreath products, Nonlinearity, 9 (1996), 559-574.
doi: 10.1088/0951-7715/9/2/016. |
[3] |
B. Dionne, M. Golubitsky and I. Stewart, Coupled cells with internal symmetry: II. Direct products, Nonlinearity, 9 (1996), 575-599.
doi: 10.1088/0951-7715/9/2/017. |
[4] |
B. Fiedler, "Global Bifurcation of Periodic Solutions with Symmetry," volume $1309$ of Lecture Notes in Mathematics, Springer, Berlin Heidelberg, 1988. |
[5] |
M. Golubitsky and I. Stewart, "The Symmetry Perspective. From Equilibrium to Chaos in Phase Space and Physical Space," volume $200$ of Progress in Mathematics, Birkhäuser, Berlin, 2002. |
[6] |
M. Golubitsky, I. Stewart and D. G. Schaeffer, "Singularities and Groups in Bifurcation Theory Vol. II," volume $69$ of Applied Mathematical Sciences, Springer, New York, 1988. |
[7] |
M. Golubitsky and I. Stewart, Nonlinear dynamics of networks: The groupoid formalism, Bulletin of the American Mathematical Society, 43 (2006), 305-364.
doi: 10.1090/S0273-0979-06-01108-6. |
[8] |
L. Gurvits, Stability of discrete linear inclusion, Linear Algebra Appl., 231 (1995), 47-85.
doi: 10.1016/0024-3795(95)90006-3. |
[9] |
P. Holmes, J. L. Lumley and G. Berkooz, "Turbulence, Coherent Structures, Dynamical Systems and Symmetry," volume II of Applied Mathematical Sciences, Cambridge University Press, 1996. |
[10] |
J. S. W. Lamb, k-symmetry and return maps of spacetime symmetric flows, Nonlinearity, 11 (1998), 601-629.
doi: 10.1088/0951-7715/11/3/011. |
[11] |
D. Liberzon, "On New Sufficient Conditions for Stability of Switched Linear Systems," Proceedings of the 2009 European Control Conference, Budapest, Hungary, Aug 2009. |
[12] |
D. Liberzon, "Switching in Systems and Control," Systems and Control: Foundations and Applications Birkhäuser, Boston, 2003. |
[13] |
J. Lygeros, K. H. Johansson, S. N. Simic, J. Zhang and S. Sastry, Dynamical properties of Hybrid automata, IEEE Transactions on Automatic Control, 48 (2003), 2-17.
doi: 10.1109/TAC.2002.806650. |
[14] |
J. Lygeros, K. H. Johansson, S. Sastry and M. Egerstedt, On the existence of executions of Hybrid automata, Proceedings of the 38th IEEE Conference on Decision and Control 1999, 3 (1999), 2249-2254. |
[15] |
S. N. Simic, K. H. Johansson, J. Lygeros and S. Sastry, Towards a geometric theory of Hybrid systems, Dynamics of Continuous, Discrete and Impulsive Systems, Series B, 12 (2005), 649-687. |
[16] |
A. van der Schaft and H. Schumacher, "An Introduction to Hybrid Dynamical Systems," Number 251 in Lecture Notes in Control and Information Sciences Springer-Verlag, London, 2000. |
show all references
References:
[1] |
M. Dellnitz and S. Hage-Packhäuser, A global symmetry framework for Hybrid dynamical systems,, preprint., ().
|
[2] |
B. Dionne, M. Golubitsky and I. Stewart, Coupled cells with internal symmetry: I. Wreath products, Nonlinearity, 9 (1996), 559-574.
doi: 10.1088/0951-7715/9/2/016. |
[3] |
B. Dionne, M. Golubitsky and I. Stewart, Coupled cells with internal symmetry: II. Direct products, Nonlinearity, 9 (1996), 575-599.
doi: 10.1088/0951-7715/9/2/017. |
[4] |
B. Fiedler, "Global Bifurcation of Periodic Solutions with Symmetry," volume $1309$ of Lecture Notes in Mathematics, Springer, Berlin Heidelberg, 1988. |
[5] |
M. Golubitsky and I. Stewart, "The Symmetry Perspective. From Equilibrium to Chaos in Phase Space and Physical Space," volume $200$ of Progress in Mathematics, Birkhäuser, Berlin, 2002. |
[6] |
M. Golubitsky, I. Stewart and D. G. Schaeffer, "Singularities and Groups in Bifurcation Theory Vol. II," volume $69$ of Applied Mathematical Sciences, Springer, New York, 1988. |
[7] |
M. Golubitsky and I. Stewart, Nonlinear dynamics of networks: The groupoid formalism, Bulletin of the American Mathematical Society, 43 (2006), 305-364.
doi: 10.1090/S0273-0979-06-01108-6. |
[8] |
L. Gurvits, Stability of discrete linear inclusion, Linear Algebra Appl., 231 (1995), 47-85.
doi: 10.1016/0024-3795(95)90006-3. |
[9] |
P. Holmes, J. L. Lumley and G. Berkooz, "Turbulence, Coherent Structures, Dynamical Systems and Symmetry," volume II of Applied Mathematical Sciences, Cambridge University Press, 1996. |
[10] |
J. S. W. Lamb, k-symmetry and return maps of spacetime symmetric flows, Nonlinearity, 11 (1998), 601-629.
doi: 10.1088/0951-7715/11/3/011. |
[11] |
D. Liberzon, "On New Sufficient Conditions for Stability of Switched Linear Systems," Proceedings of the 2009 European Control Conference, Budapest, Hungary, Aug 2009. |
[12] |
D. Liberzon, "Switching in Systems and Control," Systems and Control: Foundations and Applications Birkhäuser, Boston, 2003. |
[13] |
J. Lygeros, K. H. Johansson, S. N. Simic, J. Zhang and S. Sastry, Dynamical properties of Hybrid automata, IEEE Transactions on Automatic Control, 48 (2003), 2-17.
doi: 10.1109/TAC.2002.806650. |
[14] |
J. Lygeros, K. H. Johansson, S. Sastry and M. Egerstedt, On the existence of executions of Hybrid automata, Proceedings of the 38th IEEE Conference on Decision and Control 1999, 3 (1999), 2249-2254. |
[15] |
S. N. Simic, K. H. Johansson, J. Lygeros and S. Sastry, Towards a geometric theory of Hybrid systems, Dynamics of Continuous, Discrete and Impulsive Systems, Series B, 12 (2005), 649-687. |
[16] |
A. van der Schaft and H. Schumacher, "An Introduction to Hybrid Dynamical Systems," Number 251 in Lecture Notes in Control and Information Sciences Springer-Verlag, London, 2000. |
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