Systems theory in an analytic setting

Systems theory has almost a century of existence. The rapidly expanding research development in areas like hybrid and cyber physical systems has raised new concepts and techniques that have not been integrated in systems theory. Examples include concepts like simulation/bisimulation, hierarchical evolution and control, and so on. In their nature, these concepts are highly interdisciplinary and transdisciplinary making difficult their study in a uniform way. In this paper, we propose a new doctrine for systems theory for capturing the essential properties of systems with complex dynamics like hybrid or stochastic behaviours. Our departing point is the basic idea from specification languages like VDM and Z, and modelling languages like UML and Modelica. The fundamental concept is that of symbolic dynamics where the state space can carry not only algebraic but also an analytic structure.