Literature

The literature for hybrid systems is vast. I found choosing a single resource as the reference for our course a daunting task.

Chapter 2 of the recently published book [1] provides an up to date introduction to hybrid systems. But I am not happy about their lack of consistency in defining the roles of guards and (location/mode) invariants as the conditions for transitions. Furthermore, it is currently not available online (neither through our institutional subscription nor for free on the authors’ webpage). Among the popular references is a a thin book [2], but it is not freely available online either. Therefore, I am giving here a list of a few more recommendable references by leaders in the field.

The often cited lecture notes [3]. An updated version [4] was available online for a while, but recently the link seems to be broken (perhaps the authors have been turning them into a book). The book chapter [5] is a good and much shorter overview. It is freely available online on the authors web page. A similar overview role is played by the encyclopedia article [6], which is also freely available online.

References

[1]

H. Lin and P. J. Antsaklis, Hybrid Dynamical Systems: Fundamentals and Methods. in Advanced Textbooks in Control and Signal Processing. Cham: Springer, 2022. Accessed: Jul. 09, 2022. [Online]. Available: https://doi.org/10.1007/978-3-030-78731-8

[2]

A. J. van der Schaft and H. Schumacher, An Introduction to Hybrid Dynamical Systems. in Lecture Notes in Control and Information Sciences, no. 251. London: Springer-Verlag, 2000. Accessed: Dec. 11, 2018. [Online]. Available: https://doi.org/10.1007/BFb0109998

[3]

J. Lygeros, Lecture Notes on Hybrid Systems. 2004. Available: https://people.eecs.berkeley.edu/~sastry/ee291e/lygeros.pdf

[4]

J. Lygeros, S. Sastry, and C. Tomlin, “Hybrid Systems: Foundations, advanced topics and applications,” Jan. 2020. Available: https://www-inst.eecs.berkeley.edu/~ee291e/sp21/handouts/hybridSystems_monograph.pdf

[5]

W. P. M. H. Heemels, D. Lehmann, J. Lunze, and B. De Schutter, “Introduction to hybrid systems,” in Handbook of Hybrid Systems Control: Theory, Tools, Applications, J. Lunze and F. Lamnabhi-Lagarrigue, Eds., Cambridge University Press, 2009, pp. 3–30. doi: 10.1017/CBO9780511807930.002.

[6]

K. H. Johansson, “Hybrid control systems,” in UNESCO Encyclopedia of Life Support Systems (EOLSS), UNESCO, 2004. Accessed: Jun. 02, 2022. [Online]. Available: http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-90411