René K. Boel (Univ. of Ghent, Belgium), Oded Maler
(VERIMAG-IMAG, France), Arjan J. van der Schaft (Univ. of Twente, The Netherlands),
and Francisco J. Montoya (Univ. of Murcia, Spain)
The concept of "hybrid system" (HS for short) is used
to refer to often complex dynamic systems. Typicaly a HS model consists
of several components interacting via common dynamics (either continuous
or discrete time) or via common event driven dynamics. During the last
decade this concept has attracted the attention of many researchers who
have seen this approach as a suitable way to model and analyze complex
systems that would be quite difficult to describe otherwise. Although,
in general, the modeling and analysis of HS is a quite difficult topic
of study due to the potential complexity of such as systems, for some particular
though important classes of HS' (like piecewise-linear or switched linear
systems), some promising results have been obtained recently. This course
begins with a brief introduction to the fundamentals of discrete events
systems (DES'). Then, new features are introduced to these systems to include
some temporal (though simple) aspects, like continuous time progress. Finally,
several formalisms for modeling some specific classes of HS' are introduced.
Formal techniques for verifying properties of these models will also be
treated