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The three ages of hybrid systems: past, present and future

Eva M. Navarro-López ( University of Manchester )
What is a hybrid system? The term itself is confusing and broad, and can be used for any system consisting of elements of a different nature.

From the dynamical viewpoint, a hybrid dynamical system integrates continuous-type and discrete-event dynamics. This definition, again, can lead to a wide range of interpretations. Each interpretation has different goals and deals with specific types of problems, and reflects the  background of the researchers behind it, whether they are computer scientists, control engineers or applied mathematicians.

The hybrid-system framework should be understood as a catalyst of formal computational tools, dynamical systems theory and control engineering methodologies. This gives rise to models, behaviour analysis tools, stability definitions, control schemes, and numerical methods which are novel, and entails a better formulation of complex systems, that is, systems that are changeable and unpredictable in behaviour.

In this talk, I will present an overview of hybrid systems and the key facts about their modelling, analysis and control. I will follow the natural evolution of the theory and terminology of hybrid systems: from discontinuous/switched systems to the recent cyber-physical systems. In addition, I will present some of my current research on the redefinition of stability properties and complex dynamical behaviours of discontinuous control systems into the hybrid-automaton framework.

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