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Computing the domain of attraction of switching systems subject to non-convex constraints

Bibliographic reference Athanasopoulos, Nikolaos ; Jungers, Raphaël M.. Computing the domain of attraction of switching systems subject to non-convex constraints.Proceeding HSCC '16 Proceedings of the 19th International Conference on Hybrid Systems: Computation and Control (Vienna, Austrial, du 12/04/2016 au 14/04/2016). In: Proceeding HSCC '16, p. 51-60
Permanent URL http://hdl.handle.net/2078.1/180257
  1. G. M. Ziegler. Lectures on Polytopes, Updated Seventh Printing. Springer, 2007.
  2. Zelentsovsky A.L., Nonquadratic Lyapunov functions for robust stability analysis of linear uncertain systems, 10.1109/9.273350
  3. Vankeerberghen Guillaume, Hendrickx Julien, Jungers Raphaël M., JSR : a toolbox to compute the joint spectral radius, 10.1145/2562059.2562124
  4. A. Tarski. A decision method for elementary algebra and geometry. Rand Corporation Publication, 1948.
  5. Seidenberg A., A New Decision Method for Elementary Algebra, 10.2307/1969640
  6. Boyd Stephen, Vandenberghe Lieven, Convex Optimization, ISBN:9780511804441, 10.1017/cbo9780511804441
  7. Rota Gian–Carlo, Gilbert Strang W., A note on the joint spectral radius, 10.1016/s1385-7258(60)50046-1
  8. Putinar Mihai, , 10.1512/iumj.1993.42.42045
  9. Prajna S., Papachristodoulou A., Parrilo P.A., Introducing SOSTOOLS: a general purpose sum of squares programming solver, 10.1109/cdc.2002.1184594
  10. S. Prajna and A. Papachristodoulou. Analysis of switched and hybrid systems - beyond piecewise qudratic methods. In 22nd American Control Conference, pages 2779--2784, Denver, Colorado, 2003.
  11. Parrilo Pablo A., Jadbabaie Ali, Approximation of the joint spectral radius using sum of squares, 10.1016/j.laa.2007.12.027
  12. P. Parrilo. Structured Semidefinite Programs and Semialgebraic Geometry Methods in Robustness and Optimization. PhD thesis, California Institute of Technology, CA, USA, 2000.
  13. Papachristodoulou A., Prajna S., A tutorial on sum of squares techniques for systems analysis, 10.1109/acc.2005.1470374
  14. Molchanov A.P., Pyatnitskiy Ye.S., Criteria of asymptotic stability of differential and difference inclusions encountered in control theory, 10.1016/0167-6911(89)90021-2
  15. Lin Hai, Antsaklis Panos J., Stability and Stabilizability of Switched Linear Systems: A Survey of Recent Results, 10.1109/tac.2008.2012009
  16. Lazar M., Doban A.I., Athanasopoulos N., On stability analysis of discrete-time homogeneous dynamics, 10.1109/icstcc.2013.6688976
  17. H. Khalil. Nonlinear Systems, Third Edition. Prentice Hall, 2002.
  18. R. M. Jungers. The joint spectral radius: theory and applications, volume 385 of Lecture Notes in Control and Information Sciences. Springer, 2008.
  19. Johansson M., Rantzer A., Computation of piecewise quadratic Lyapunov functions for hybrid systems, 10.1109/9.664157
  20. Tingshu Hu, Zongli Lin, Composite quadratic Lyapunov functions for constrained control systems, 10.1109/tac.2003.809149
  21. M. Herceg, M. Kvasnica, C. N. Jones and M. Morari Multi-parametric toolbox 3.0. In European Control Conference, pages 502--510, Zurich, Switzerland, 2013.
  22. J. C. Hennet. Discrete Time Constrained Linear Systems. Control and Dynamic Systems, Leondes Ed. Academic Press, 71:157--213, 1995.
  23. Gutman P.-O., Cwikel M., An algorithm to find maximal state constraint sets for discrete-time linear dynamical systems with bounded controls and states, 10.1109/tac.1987.1104567
  24. Gilbert E.G., Tan K.T., Linear systems with state and control constraints: the theory and application of maximal output admissible sets, 10.1109/9.83532
  25. E. G. Gilbert and K. T. Tan. Linear systems with state and control constraints: the theory and application of maximal output admissible sets. IEEE Transactions on Automatic Control, 36(9):1008--1020, 1991.
  26. K. Fukuda. Frequently asked questions in polyhedral computation. Official website: http://www.ifor.math.ethz.ch/~fukuda/polyfaq/polyfaq.html.
  27. Boyd Stephen, El Ghaoui Laurent, Feron Eric, Balakrishnan Venkataramanan, Linear Matrix Inequalities in System and Control Theory, ISBN:9780898714852, 10.1137/1.9781611970777
  28. Blondel Vincent D., Nesterov Yurii, Computationally Efficient Approximations of the Joint Spectral Radius, 10.1137/040607009
  29. Semidefinite Optimization and Convex Algebraic Geometry, ISBN:9781611972283, 10.1137/1.9781611972290
  30. F. Blanchini and S. Miani. Set-theoretic methods in control. Systems & Control: Foundations & Applications. Birkhäuser, Boston, MA, 2008.
  31. Blanchini F., Set invariance in control, 10.1016/s0005-1098(99)00113-2
  32. Bitsoris George, Olaru Sorin, Further results on the linear constrained regulation problem, 10.1109/med.2013.6608818
  33. Bitsoris Georges, On the positive invariance of polyhedral sets for discrete-time systems, 10.1016/0167-6911(88)90065-5
  34. Bertsekas D., Infinite time reachability of state-space regions by using feedback control, 10.1109/tac.1972.1100085
  35. Belta C., Isler V., Pappas G.J., Discrete abstractions for robot motion planning and control in polygonal environments, 10.1109/tro.2005.851359
  36. Barber C. Bradford, Dobkin David P., Huhdanpaa Hannu, The quickhull algorithm for convex hulls, 10.1145/235815.235821
  37. J. P. Aubin, A. M. Bayen, and P. Saint-Pierre. Viability Theory: New Directions. Springer, Heidelber Dordrecht London New York , 2011.
  38. N. Athanasopoulos, M. Lazar, and G. Bitsoris. Property-preserving convergent sequences of invariant sets for linear discrete-time systems. In 21st International Symposium on Mathematical Theory of Networks and Systems, pages 1280--1286, Groningen, The Netherlands, 2014.
  39. A. A. Ahmadi and R. M. Jungers. Switched stability of nonlinear systems via SOS-convex Lyapunov functions and semidefinite programming . In American Control Conference, pages 2686--2700, Boston, MA, USA, 2005.