Hybrid dynamical systems: An introduction to control and verification

Foundations and Trends in Systems and Control

Volumn 1, Issue 1, 2014, Pages 1-172

  Lin, Hai ^a   Antsaklis, Panos J ^a  

^a UNIVERSITY OF NOTRE DAME   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER AIDED ANALYSIS; EMBEDDED SYSTEMS; HYBRID SYSTEMS; INDUSTRIAL RESEARCH; MANUFACTURE; STABILIZATION;

COMPUTER AIDED VERIFICATIONS; CONTINUOUS VARIABLES; HYBRID DYNAMICAL SYSTEMS; INTELLIGENCE COMMUNITIES; RESEARCH ACTIVITIES; STABILITY ANALYSIS; SUPERVISORY CONTROL; TRAFFIC MANAGEMENT;

COMPUTER CONTROL SYSTEMS;

EID: 84938385099     PISSN: 23256818     EISSN: 23256826     Source Type: Journal    
DOI: 10.1561/2600000001     Document Type: Article

References (167)

1. R. Alur and D. Dill. The theory of timed automata. Theoretical Computer Science, 126:193-235, 1994.
2. R. Alur and T. Henzinger. Modularity for timed and hybrid systems. In A. Mazurkiewicz and J. Winkowski, editors, CONCUR '97: Concurrency Theory, volume 1243 of Lecture Notes in Computer Science, pages 74-88. Springer Berlin Heidelberg, 1997. ISBN 978-3-540-63141-5.
3. R. Alur, C. Courcoubetis, and D. Dill. Model-checking for real-time systems. In Logic in Computer Science, 1990. LICS '90, pages 414-425, Jun 1990.
4. R. Alur, C. Courcoubetis, N. Halbwachs, T. Henzinger, P. H. Ho, X. Nicollin, A. Olivero, J. Sifakis, and S. Yovine. The algorithmic analysis of hybrid systems. Theoretical Computer Science, 138:3-34, 1995.
5. R. Alur, T. Henzinger, G. Lafferriere, and G. J. Pappas. Discrete abstractions of hybrid systems. In P. J. Antsaklis, editor, Proceedings of the IEEE: Special issue on hybrid systems, volume 88, pages 971-984. IEEE Press, 2000a.
6. Rajeev Alur, Costas Courcoubetis, ThomasA. Henzinger, and Pei-Hsin Ho. Hybrid automata: An algorithmic approach to the specification and verification of hybrid systems. In RobertL. Grossman, Anil Nerode, Anders P. Ravn, and Hans Rischel, editors, Hybrid Systems, volume 736 of Lecture Notes in Computer Science, pages 209-229. Springer BerlinHeidelberg, 1993. ISBN 978-3-540-57318-0.
7. Rajeev Alur, Radu Grosu, Yerang Hur, Vijay Kumar, and Insup Lee. Modular specification of hybrid systems in charon. In Hybrid Systems: Computation and Control, pages 6-19. Springer, 2000b.
8. P. J. Antsaklis and A. Nerode. Hybrid control systems: An introductory discussion to the special issue. IEEE Trans. Automat. Contr., 43(4):457-460, 1998.
9. Panos J Antsaklis. A brief introduction to the theory and applications of hybrid systems. In Proc IEEE, Special Issue on Hybrid Systems: Theory and Applications, 2000.
10. Eugene Asarin and Oded Maler. As soon as possible: Time optimal control for timed automata. In Hybrid Systems: Computation and Control, pages 19- 30. Springer, 1999.
11. Eugene Asarin, Thao Dang, and Oded Maler. The d/dt tool for verification of hybrid systems. In Computer Aided Verification, pages 365-370. Springer, 2002.
12. J. Aubin, J. Lygeros, M. Quincampoix, S. Sastry, and N. Seube. Impulse differential inclusions: A viability approach to hybrid systems. IEEE Trans. Automat. Contr., 47(1):2-20, 2002.
13. R. Baheti and H. Gill. Cyber-physical systems. The Impact of Control Technology, pages 161-166, 2011.
14. C. Baier and J. P. Katoen. Principles of model checking. MIT press Cambridge, 2008.
15. A. Balluchi, L. Benvenuti, M.D. Di Benedetto, C. Pinello, and A.L. Sangiovanni-Vincentelli. Automotive engine control and hybrid systems: challenges and opportunities. Proceedings of the IEEE, 88(7):888-912, July 2000.
16. Gerd Behrmann, Alexandre David, and Kim G Larsen. A tutorial on uppaal. In Formal methods for the design of real-time systems, pages 200-236. Springer, 2004.
17. C. Belta and L. C G J M Habets. Controlling a class of nonlinear systems on rectangles. Automatic Control, IEEE Transactions on, 51(11):1749-1759, Nov 2006.
18. C. Belta, A. Bicchi, M. Egerstedt, E. Frazzoli, E. Klavins, and G.J. Pappas. Symbolic planning and control of robot motion. Robotics and Automation Magazine, IEEE, 14(1):61-70, March 2007.
19. A. Bemporad andM. Morari. Control of systems integrating logic, dynamics, and constraints. Automatica, 35(3):407-427, 1999.
20. A. Bemporad, F. Borrelli, and M. Morari. On the optimal control law for linear discrete time hybrid systems. In Hybrid systems: Computation and control, volume 2289 of Lecture Notes in Computer Science, pages 105-119. Springer, 2002.
21. Alberto Bemporad, Giancarlo Ferrari-Trecate, and ManfredMorari. Observability and controllability of piecewise affine and hybrid systems. IEEE transactions on automatic control, 45(10):1864-1876, 2000.
22. S. C. Bengea and R. A. DeCarlo. Optimal control of switching systems. Automatica, 41(1):11-27, January 2005.
23. Beatrice Berard, Michel Bidoit, Alain Finkel, Francois Laroussinie, Antoine Petit, Laure Petrucci, and Philippe Schnoebelen. Systems and software verification: model-checking techniques and tools. Springer Publishing Company, Incorporated, 2010.
24. A. Bhaya and F. Mota. Equivalence of stability concepts for discrete timevarying systems. Int. J. Robust and Nonlin. Contr., 4:725-740, 1994.
25. F. Borrelli. Constrained Optimal Control of Linear and Hybrid Systems, volume 290 of Lecture Notes in Control and Information Sciences. Springer-Verlag, 2003.
26. Francesco Borrelli, Mato Baotić, Alberto Bemporad, and Manfred Morari. Dynamic programming for constrained optimal control of discrete-time linear hybrid systems. Automatica, 41(10):1709-1721, 2005.
27. S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan. Linear Matrix Inequalities in System and Control Theory. SIAM, 1994.
28. B.A. Brandin and W.M. Wonham. Supervisory control of timed discreteevent systems. Automatic Control, IEEE Transactions on, 39(2):329-342, 1994.
29. M. S. Branicky. Multiple lyapunov functions and other analysis tools for switched and hybrid systems. IEEE Trans. Automat. Contr., 43(4):475-482, 1998.
30. M.S. Branicky, V.S. Borkar, and S.K. Mitter. A unified framework for hybrid control: model and optimal control theory. Automatic Control, IEEE Transactions on, 43(1):31-45, 1998.
31. M.S. Branicky, M.M. Curtiss, J. Levine, and S. Morgan. Sampling-based planning, control and verification of hybrid systems. IEE Proceedings - Control Theory and Applications, 153:575-590(15), September 2006.
32. R. W. Brockett. Asymptotic stability and feedback stabilization. In R. W. Brockett, R. S. Millman, and H. J. Sussmann, editors, Differential Geometric Control Theory, pages 181-191. Boston, MA: Birkhuser, 1983.
33. C. G. Cassandras and S. Lafortune. Introduction to Discrete Event Systems (2nd Edition). Springer-Verlag, 2008.
34. C.G. Cassandras, D.L. Pepyne, and Y. Wardi. Optimal control of a class of hybrid systems. IEEE Trans. Automat. Contr., 46(3):398-415, 2001.
35. Christos G Cassandras and John Lygeros. Stochastic hybrid systems. CRC Press, 2010.
36. A. Chutinan and B. H. Krogh. Computational techniques for hybrid system verification. IEEE Trans. Automat. Contr., 48(1):64-75, 2003.
37. Alessandro Cimatti, Edmund Clarke, Enrico Giunchiglia, Fausto Giunchiglia, Marco Pistore, Marco Roveri, Roberto Sebastiani, and Armando Tacchella. Nusmv 2: An opensource tool for symbolic model checking. In Computer Aided Verification, pages 359-364. Springer, 2002.
38. E. M. Clarke, O. Grumberg, and D. Peled. Model Checking. MIT press, 1999.
39. Edmund M. Clarke, E Allen Emerson, and A Prasad Sistla. Automatic verification of finite-state concurrent systems using temporal logic specifications. ACM Transactions on Programming Languages and Systems (TOPLAS), 8(2):244-263, 1986.
40. Jose ER Cury, Bruce H Krogh, and Toshihiko Niinomi. Synthesis of supervisory controllers for hybrid systems based on approximating automata. Automatic Control, IEEE Transactions on, 43(4):564-568, 1998.
41. J. Daafouz, R. Riedinger, and C. Iung. Stability analysis and control synthesis for switched systems: a switched lyapunov function approach. IEEE Trans. Automat. Contr., 47(11):1883-1887, 2002.
42. Thao Dang, Alexandre Donze, Oded Maler, and Noa Shalev. Sensitive statespace exploration. In Decision and Control, 2008. CDC 2008. 47th IEEE Conference on, pages 4049-4054. IEEE, 2008.
43. Tuhin Das and Ranjan Mukherjee. Optimally switched linear systems. Automatica, 44(5):1437-1441, 2008.
44. H. De Jong. Modeling and simulation of genetic regulatory systems: a literature review. Journal of computational biology, 9(1):67-103, 2002.
45. R. A. DeCarlo, M. S. Branicky, S. Pettersson, and B. Lennartson. Perspectives and results on the stability and stabilizability of hybrid systems. In P. J. Antsaklis, editor, Proceedings of the IEEE: Special issue on hybrid systems, volume 88, pages 1069-1082. IEEE Press, 2000.
46. Akash Deshpande, Aleks GAullAij, and Pravin Varaiya. Shift: A formalism and a programming language for dynamic networks of hybrid automata. In Panos Antsaklis, Wolf Kohn, Anil Nerode, and Shankar Sastry, editors, Hybrid Systems IV, volume 1273 of Lecture Notes in Computer Science, pages 113-133. Springer Berlin Heidelberg, 1997.
47. Stephen Edwards, Luciano Lavagno, Edward A Lee, and Alberto Sangiovanni-Vincentelli. Design of embedded systems: Formal models, validation, and synthesis. Readings in hardware/software co-design, page 86, 2001.
48. Magnus Egerstedt. Behavior based robotics using hybrid automata. In Nancy Lynch and BruceH. Krogh, editors, Hybrid Systems: Computation and Control, volume 1790 of Lecture Notes in Computer Science, pages 103-116. Springer Berlin Heidelberg, 2000.
49. Magnus Egerstedt, Yorai Wardi, and Henrik Axelsson. Transition-time optimization for switched-mode dynamical systems. Automatic Control, IEEE Transactions on, 51(1):110-115, 2006.
50. E Allen Emerson. Temporal and modal logic. Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics (B), 995:1072, 1990.
51. S. Engell, S. Kowalewski, C. Schulz, and O. Stursberg. Continuous-discrete interactions in chemical processing plants. Proceedings of the IEEE, 88(7): 1050-1068, July 2000.
52. G. E. Fainekos, A. Girard, H. Kress-Gazit, and G. J. Pappas. Temporal logic motion planning for dynamic robots. Automatica, 45(2):343-352, 2009. ISSN 0005-1098.
53. E. Feron. Quadratic stabilizability of switched systems via state and output feedback. Technical Report CICS-P-468, MIT, 1996.
54. Giancarlo Ferrari-Trecate, Marco Muselli, Diego Liberati, and Manfred Morari. A clustering technique for the identification of piecewise affine systems. Automatica, 39(2):205-217, 2003.
55. Goran Frehse, Colas Le Guernic, Alexandre Donze, Scott Cotton, Rajarshi Ray, Olivier Lebeltel, Rodolfo Ripado, Antoine Girard, Thao Dang, and Oded Maler. Spaceex: Scalable verification of hybrid systems. In Computer Aided Verification, pages 379-395. Springer, 2011.
56. Paul Gastin and Denis Oddoux. Fast ltl to buchi automata translation. In Computer Aided Verification, pages 53-65. Springer, 2001.
57. A. Girard and G. J. Pappas. Approximation metrics for discrete and continuous systems. Automatic Control, IEEE Transactions on, 52(5):782-798, 2007.
58. A. Girard and G. J. Pappas. Hierarchical control system design using approximate simulation. Automatica, 45(2):566-571, 2009. ISSN 0005-1098.
59. Antoine Girard and George J Pappas. Approximation metrics for discrete and continuous systems. 2005.
60. R. Goebel, R. Sanfelice, and A. R. Teel. Hybrid dynamical systems. IEEE Control Systems Magazine, 29(2):28'lC93, 2009.
61. R. Goebel, R. G. Sanfelice, and A. R. Teel. Hybrid Dynamical Systems: modeling, stability, and robustness. Princeton University Press, 2012.
62. Humberto Gonzalez, Ramanarayan Vasudevan, Maryam Kamgarpour, S Shankar Sastry, Ruzena Bajcsy, and Claire Tomlin. A numerical method for the optimal control of switched systems. In Decision and Control (CDC), 2010 49th IEEE Conference on, pages 7519-7526. IEEE, 2010.
63. L. Habets and Jan H. van Schuppen. A control problem for affine dynamical systems on a full-dimensional polytope. Automatica, 40(1):21-35, 2004.
64. LCGJM Habets, Pieter J Collins, and Jan H van Schuppen. Reachability and control synthesis for piecewise-affine hybrid systems on simplices. Automatic Control, IEEE Transactions on, 51(6):938-948, 2006a.
65. LCGJM Habets, M Kloetzer, and Calin Belta. Control of rectangular multiaffine hybrid systems. In Decision and Control, 2006 45th IEEE Conference on, pages 2619-2624. IEEE, 2006b.
66. S. Hedlund and A. Rantzer. Cdp tool: A matlab tool for optimal control of hybrid systems. department of automatic control. In Lund Institute of Technology, 1999.
67. S. Hedlund and A. Rantzer. Convex dynamic programming for hybrid systems. Automatic Control, IEEE Transactions on, 47(9):1536-1540, Sep 2002.
68. W. PMH Heemels, B. De Schutter, and A. Bemporad. Equivalence of hybrid dynamical models. Automatica, 37(7):1085-1091, 2001.
69. T. Henzinger. Hybrid automata with finite bisimulations. In Z. Fullop and G. Gecgeg, editors, ICALP'95: Automata, Languages, and Programming. Springer-Verlag, 1995.
70. T. Henzinger. The theory of hybrid automata. InM.K. Inan and R.P. Kurshan, editors, Verification of Digital and Hybrid Systems, volume 170 of NATO ASI Series, pages 265-292. Springer Berlin Heidelberg, 2000.
71. T. Henzinger, P. Ho, and H. Wong-Toi. Hytech: A model checker for hybrid systems. In Computer aided verification, pages 460-463. Springer, 1997.
72. T. Henzinger, P. W. Kopke, A. Puri, and P. Varaiya. What's decidable about hybrid automata? Journal of Computer and System Sciences, 57:94-124, 1998.
73. Thomas AHenzinger, PeterWKopke, Anuj Puri, and Pravin Varaiya.What's decidable about hybrid automata? In Proceedings of the twenty-seventh annual ACM symposium on Theory of computing, pages 373-382. ACM, 1995.
74. J. P. Hespanha. Stabilization through hybrid control. In H. Unbehauen, editor, Encyclopedia of Life Support Systems (EOLSS), volume Control Systems, Robotics, and Automation. Oxford, UK, 2004a.
75. J. P. Hespanha and A. S. Morse. Stability of switched systems with average dwell-time. In Proc. 38th IEEE Conf. Decision Control, pages 2655-2660, 1999.
76. J. P. Hespanha, D. Liberzon, and A. S. Morse. Logic-based switching control of a nonholonomic system with parametricmodeling uncertainty. Systems & Control Letters, 38(3):167-177, 1999.
77. J. P. Hespanha, D. Liberzon, D. Angeli, and E. D. Sontag. Nonlinear normobservability notions and stability of switched systems. IEEE Trans. Automat. Contr., 52(2):154-168, 2005.
78. Joao P Hespanha. Stochastic hybrid systems: Application to communication networks. In Hybrid systems: computation and control, pages 387-401. Springer, 2004b.
79. Gerard J Holzmann. The model checker spin. IEEE Transactions on software engineering, 23(5):279-295, 1997.
80. J. E. Hopcroft, R. Motwani, and J. D. Ullman. Introduction to Automata Theory, Languages, and Computation. Prentice Hall, third edition, 2006.
81. Jianghai Hu, John Lygeros, and Shankar Sastry. Towards a theory of stochastic hybrid systems. In Hybrid Systems: Computation and Control, pages 160- 173. Springer, 2000.
82. J. Imura and A. van der Schaft. Characterization of well-posedness of piecewise-linear systems. IEEE Trans. Automat. Contr., 45(9):1600-1619, 2000.
83. Karl Henrik Johansson, Magnus Egerstedt, John Lygeros, and Shankar Sastry. On the regularization of zeno hybrid automata. Systems & Control Letters, 38(3):141-150, 1999.
84. M. Johansson. Piecewise Linear Control Systems: A Computational Approach, volume 284 of Lecture Notes in Control and Information Sciences. Springer- Verlag, 2003a.
85. M. K.-J. Johansson, editor. Piecewise Linear Control Systems: A Computational Approach, volume 284 of Lecture Notes in Control and Information Sciences. Springer-Verlag, 2003b.
86. Aleksandar Lj Juloski, Siep Weiland, and WPMH Heemels. A bayesian approach to identification of hybrid systems. Automatic Control, IEEE Transactions on, 50(10):1520-1533, 2005.
87. Matt Kaufmann, J Strother Moore, and Panagiotis Manolios. Computer-aided reasoning: an approach. Kluwer Academic Publishers, 2000.
88. Hassan K Khalil and JW Grizzle. Nonlinear systems, volume 3. Prentice hall Upper Saddle River, 2002.
89. C. King and R. Shorten. A singularity test for the existence of common quadratic lyapunov functions for pairs of stable LTI systems. In Proc. 2004 American Contr. Conf., pages 3881-3884, 2004.
90. M. Kloetzer and C. Belta. A fully automated framework for control of linear systems from temporal logic specifications. Automatic Control, IEEE Transactions on, 53(1):287-297, 2008.
91. X.D. Koutsoukos, P.J. Antsaklis, J.A. Stiver, and M.D. Lemmon. Supervisory control of hybrid systems. Proceedings of the IEEE, 88(7):1026-1049, July 2000.
92. Marta Kwiatkowska, Gethin Norman, and David Parker. Prism: Probabilistic symbolic model checker. In Computer performance evaluation: modelling techniques and tools, pages 200-204. Springer, 2002.
93. G. Lafferriere, G. J. Pappas, and S. Sastry. O-minimal hybrid systems. Mathematics of control, signals and systems, 13(1):1-21, 2000.
94. Carl W Lee. Subdivisions and triangulations of polytopes. In Handbook of discrete and computational geometry, pages 271-290. CRC Press, Inc., 1997.
95. E.A. Lee. Cyber physical systems: Design challenges. In Object Oriented Real- Time Distributed Computing (ISORC), 2008 11th IEEE International Symposium on, pages 363-369, May 2008.
96. Domine MW Leenaerts and Wim MG Van Bokhoven. Piecewise linear modeling and analysis. Springer, 1998.
97. M. D. Lemmon, K. He, and I. Markovsky. Supervisory hybrid systems. Control Systems, IEEE, 19(4):42-55, 1999.
98. D. Liberzon. Switching in Systems and Control. Birkhauser, Boston, 2003.
99. D. Liberzon and A. S. Morse. Basic problems in stability and design of switched systems. IEEE Contr. Syst. Magazine, 19(5):59-70, 1999.
100. D. Liberzon, J. P. Hespanha, and A. S. Morse. Stability of switched linear systems: A lie-algebraic condition. Syst. Contr. Lett., 37(3):117-122, 1999.
101. H. Lin and P. J. Antsaklis. Switching stabilizability for continuous-time uncertain switched linear systems. IEEE Trans. Automat. Contr., 52(4):633-646, 2007.
102. H. Lin and P.J. Antsaklis. Stability and stabilizability of switched linear systems: A survey of recent results. Automatic Control, IEEE Transactions on, 54(2):308-322, 2009.
103. Hai Lin and Panos J Antsaklis. Hybrid state feedback stabilization with l 2 performance for discrete-time switched linear systems. International Journal of Control, 81(7):1114-1124, 2008.
104. Ji-Nan Lin and Rolf Unbehauen. Canonical piecewise-linear approximations. IEEE Transactions on circuits and systems. I: Fundamental theory and applications, 39(8):697-699, 1992.
105. Jie Liu, Xiaojun Liu, Tak-Kuen J. Koo, B. Sinopoli, S. Sastry, and E.A. Lee. A hierarchical hybrid system model and its simulation. In Decision and Control, 1999. Proceedings of the 38th IEEE Conference on, volume 4, pages 3508-3513 vol.4, 1999.
106. J. Lygeros, S. Sastry, and C. Tomlin. The Art of Hybrid Systems. 2001. URL http://robotics.eecs.berkeley.edu/~sastry/ee291e/book.pdf.
107. J. Lygeros, K.H. Johansson, S.N. Simic, Jun Zhang, and S.S. Sastry. Dynamical properties of hybrid automata. Automatic Control, IEEE Transactions on, 48 (1):2-17, 2003.
108. N. Lynch, R. Segala, and F. Vaandrager. Hybrid I/O automata. Information and Computation, 185(1):103-157, 2003.
109. Oded Maler, Amir Pnueli, and Joseph Sifakis. On the synthesis of discrete controllers for timed systems. In STACS 95, pages 229-242. Springer, 1995.
110. MichaelMargaliot and Daniel Liberzon. Lie-algebraic stability conditions for nonlinear switched systems and differential inclusions. Systems & control letters, 55(1):8-16, 2006.
111. A. N. Michel. Recent trends in the stability analysis of hybrid dynamical systems. IEEE Trans. Circuits Syst. I, 46(1):120-134, 1999.
112. R. Milner. Communication and Concurrency. Prentice-Hall, Inc., Upper Saddle River, NJ, USA, 1989.
113. Eduardo Mojica-Nava, Nicanor Quijano, and Naly Rakoto-Ravalontsalama. A polynomial approach for optimal control of switched nonlinear systems. International Journal of Robust and Nonlinear Control, 2013.
114. A. P. Molchanov and D. Liu. Robust absolute stability of time-varying nonlinear discrete-time systems. IEEE Trans. Circuits Syst. I, 49(8):1129-1137, 2002.
115. A. P. Molchanov and E. Pyatnitskiy. Criteria of asymptotic stability of differential and difference inclusions encountered in control theory. Systems & Control Letters, 13:59-64, 1989.
116. A. S. Morse. Supervisory control of families of linear set-point controllers - part 1: Exact matching. IEEE Trans. Automat. Contr., 41(10):1413-1431, 1996.
117. K. S. Narendra and J. Balakrishnan. A common lyapunov function for stable LTI systems with commuting a-matrices. IEEE Trans. Automat. Contr., 39 (12):2469-2471, 1994.
118. Truong Nghiem, Sriram Sankaranarayanan, Georgios Fainekos, Franjo Ivancić, Aarti Gupta, and George J Pappas. Monte-carlo techniques for falsification of temporal properties of non-linear hybrid systems. In Proceedings of the 13th ACM international conference on Hybrid systems: computation and control, pages 211-220. ACM, 2010.
119. A. Papachristodoulou and S. Prajna. A tutorial on sum of squares techniques for systems analysis. In Proc. 2005 American Control Conf., 2005.
120. Antonis Papchristodoulou and Stephen Prajna. Robust stability analysis of nonlinear hybrid systems. IEEE Transactions on Automatic Control, 54(5): 1034-1041, 2009.
121. D.L. Pepyne and C.G. Cassandras. Optimal control of hybrid systems in manufacturing. Proceedings of the IEEE, 88(7):1108-1123, July 2000.
122. S. Pettersson. Synthesis of switched linear systems. In Proc. 42nd IEEE Conf. Decision Control, pages 5283-5288, 2003.
123. S. Pettersson and B. Lennartson. Stabilization of hybrid systems using a min-projection strategy. In Proc. 2001 American Contr. Conf., pages 223-228, 2001.
124. S. Pettersson and B. Lennartson. Hybrid system stability and robustness verification using linear matrix inequalities. Inter. J. Contr., 75(16-17):1335-1355, 2002.
125. Erion Plaku, Lydia E Kavraki, and Moshe Y Vardi. Falsification of ltl safety properties in hybrid systems. International Journal on Software Tools for Technology Transfer, 15(4):305-320, 2013.
126. Amir Pnueli. The temporal logic of programs. In Foundations of Computer Science, 1977., 18th Annual Symposium on, pages 46-57, Oct 1977.
127. Amir Pnueli and Roni Rosner. On the synthesis of a reactive module. In Proceedings of the 16th ACM SIGPLAN-SIGACT symposium on Principles of programming languages, pages 179-190. ACM, 1989.
128. G Pola, ML Bujorianu, J Lygeros, and MDD Benedetto. Stochastic hybrid models: An overview. In Proc. IFAC Conf. Anal. Design Hybrid Syst, pages 45-50, 2003.
129. S. Prajna and A. Papachristodoulou. Analysis of switched and hybrid systems - beyond piecewise quadratic methods. In Proc. 42nd IEEE Conf. Decision Control, pages 2779-2784, 2003.
130. Stephen Prajna andAli Jadbabaie. Safety verification of hybrid systems using barrier certificates. In Hybrid Systems: Computation and Control, pages 477- 492. Springer, 2004.
131. Michael Melholt Quottrup, Thomas Bak, and RI Zamanabadi. Multi-robot planning: A timed automata approach. In Robotics and Automation, 2004. Proceedings. ICRA'04. 2004 IEEE International Conference on, volume 5, pages 4417-4422. IEEE, 2004.
132. Jorg Raisch and Siu D O'Young. Discrete approximation and supervisory control of continuous systems. Automatic Control, IEEE Transactions on, 43 (4):569-573, 1998.
133. P. Ramadge and W. M. Wonham. The control of discrete event systems. Proceedings of the IEEE, 77(1):81-98, 1989.
134. Peter J Ramadge and W Murray Wonham. Supervisory control of a class of discrete event processes. SIAM journal on control and optimization, 25(1): 206-230, 1987.
135. A. Rantzer and M. Johansson. Piecewise linear quadratic optimal control. IEEE Trans. Automat. Contr., 45(4):629-637, 2000.
136. Mark Reynolds. Continuous temporal models. In AI 2001: Advances in Artificial Intelligence, pages 414-425. Springer, 2001.
137. Jacob Roll, Alberto Bemporad, and Lennart Ljung. Identification of piecewise affine systems via mixed-integer programming. Automatica, 40(1):37-50, 2004.
138. A. van der Schaft and H. Schumacher. An Introduction to Hybrid Dynamical Systems, volume 251 of Lecture Notes in Control and Information Sciences. Springer-Verlag, London, 2000.
139. M Shahid Shaikh and Peter E Caines. On the hybrid optimal control problem: theory and algorithms. Automatic Control, IEEE Transactions on, 52(9):1587-1603, 2007.
140. Robert Shorten, Fabian Wirth, Oliver Mason, Kai Wulff, and Christopher King. Stability criteria for switched and hybrid systems. SIAM review, 49(4):545-592, 2007.
141. B Izaias Silva, Keith Richeson, Bruce Krogh, and Alongkrit Chutinan. Modeling and verifying hybrid dynamic systems using checkmate. In Proceedings of 4th International Conference on Automation of Mixed Processes, pages 323-328, 2000.
142. E. Skafidas, R. J. Evans, A. V. Savkin, and I. R. Petersen. Stability results for switched controller systems. Automatica, 35(4):553-564, 1999.
143. Eduardo Sontag. Nonlinear regulation: The piecewise linear approach. Automatic Control, IEEE Transactions on, 26(2):346-358, 1981.
144. Eduardo D Sontag. Mathematical control theory: deterministic finite dimensional systems, volume 6. Springer, 1998.
145. Zhendong Sun, Shuzhi Sam Ge, and Tong Heng Lee. Controllability and reachability criteria for switched linear systems. Automatica, 38(5):775-786, 2002.
146. H.J. Sussmann. A maximum principle for hybrid optimal control problems. In Decision and Control, 1999. Proceedings of the 38th IEEE Conference on, volume 1, pages 425-430 vol.1, 1999.
147. P. Tabuada. Verification and Control of Hybrid Systems: A Symbolic Approach. Springer, Springer New York, 2009.
148. Paulo Tabuada. An approximate simulation approach to symbolic control. Automatic Control, IEEE Transactions on, 53(6):1406-1418, 2008.
149. Wolfgang Thomas. On the synthesis of strategies in infinite games. In STACS 95, pages 1-13. Springer, 1995.
150. C. Tomlin, G.J. Pappas, and S. Sastry. Conflict resolution for air traffic management: a study in multiagent hybrid systems. Automatic Control, IEEE Transactions on, 43(4):509-521, Apr 1998.
151. Claire J Tomlin, Ian Mitchell, Alexandre M Bayen, and Meeko Oishi. Computational techniques for the verification of hybrid systems. Proceedings of the IEEE, 91(7):986-1001, 2003.
152. Fabio Danilo Torrisi and Alberto Bemporad. Hysdel-a tool for generating computational hybrid models for analysis and synthesis problems. Control Systems Technology, IEEE Transactions on, 12(2):235-249, 2004.
153. Moshe Y Vardi. An automata-theoretic approach to linear temporal logic. In Logics for concurrency, pages 238-266. Springer, 1996.
154. YoraiWardi and Magnus Egerstedt. Algorithm for optimal mode scheduling in switched systems. In American Control Conference (ACC), 2012, pages 4546-4551. IEEE, 2012.
155. M. A. Wicks and R. A. DeCarlo. Solution of coupled lyapunov equations for the stabilization of multi-modal linear systems. In Proc. 1997 American Contr. Conf., pages 1709-1713, 1997.
156. M. A. Wicks, P. Peleties, and R. A. DeCarlo. Switched controller design for the quadratic stabilization of a pair of unstable linear systems. European J. Control, 4:140-147, 1998.
157. H. Witsenhausen. A class of hybrid-state continuous-time dynamic systems. Automatic Control, IEEE Transactions on, 11(2):161-167, Apr 1966.
158. H. Wong-Toi and G. Hoffmann. The control of dense real-time discrete event systems. In Decision and Control, 1991., Proceedings of the 30th IEEE Conference on, pages 1527-1528. IEEE, 1991.
159. Guangming Xie and Long Wang. Controllability and stabilizability of switched linear-systems. Systems & Control Letters, 48(2):135-155, 2003.
160. X. Xu and P. J. Antsaklis. Results and perspectives on computational methods for optimal control of switched systems. In Hybrid Systems: Computation and Control, pages 540-555. Springer, 2003.
161. X. Xu and P. J. Antsaklis. Optimal control of switched systems based on parameterization of the switching instants. IEEE Trans. Automat. Contr., 49 (1):2-16, 2004.
162. H. Ye, A. N. Michel, and L. Hou. Stability theory for hybrid dynamical systems. IEEE Trans. Automat. Contr., 43(4):461-474, 1998.
163. Sergio Yovine. Kronos: A verification tool for real-time systems. International Journal on Software Tools for Technology Transfer (STTT), 1(1):123-133, 1997.
164. G. Zhai, B. Hu, K. Yasuda, and A. N. Michel. Qualitative analysis of discretetime switched systems. In Proc. 2002 American Contr. Conf., volume 3, pages 1880-1885, 2002.
165. G. Zhai, H. Lin, and P. J. Antsaklis. Quadratic stabilizability of switched linear systems with polytopic uncertainties. Inter. J. Contr., 76(7):747-753, 2003.
166. F. Zhu and P. J. Antsaklis. Optimal control of switched hybrid systems: a brief survey. ISIS Tech. Report (to appera in Discrete Event Dynamic Systems), 3, 2011.
167. Gunter M Ziegler. Lectures on polytopes, volume 152. Springer, 1995.