The methods for hybrid systems are distributed across a wide
spectrum, ranging from methods known in the discrete (cyber-)domain
at one end, to traditional approaches for the continuous physical
systems at the other. Rooted at opposite ends, both computer
scientists and control theorists have made significant
contributions to the field of hybrid systems by extending
traditional methods from the traditional discrete or continuous
domain to deal with hybrid systems. However, in general, there has
been little work on integrating methods from these two domains.
This is possibly because the formal methods pursued in computer
science traditionally lie in the realm of discrete mathematics,
while control theory approaches lie mainly in the realm of
continuous mathematics. A noticeable trend in the recent hybrid
system literature emphasizes the synthesis of hybrid controllers
for continuous or hybrid dynamical systems to satisfy complicated
temporal logic specifications. This is known as symbolic control or
hybrid supervisory control, which can be seen as a crosstalk
between these two schools of thoughts. Hybrid Dynamical Systems
balances the emphasis on methods from both computer science and
control theory, and gives the readers a complete picture of the
whole field of hybrid dynamical systems. As well as providing a
concise overview for a researcher in the field, the tutorial style
makes it suitable for use in a course and by students.
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