Mikael Kurula - Åbo Akademi

Chapter 7
A few ideas for the future
The study of state/signal systems and irregular interconnection of infinite-dimensional
systems has merely been started and much remains to be done. Many questions remain
to be answered in connection with stability, the properties of the state/signal dual and
the properties of impedance representations. The articles by Arov and Staffans on
discrete-time state/signal systems contain a large number of results, which should be
considered in continuous time as well. In particular the frequency-domain behaviour
of state/signal systems should be worked out.
Also regarding interconnection there is much work undone. The results presented
in [KZvdSB09] should be generalised to more general types of interconnection. One
may also ask when an interconnection of two state/signal systems is a regular feedback
interconnection of two input/state/output systems and which system behaviours
can be achieved through interconnection with a controller. The finite-dimensional
formulations of these problems can be found in [JWBT05]. A study in which cases
well-posedness is preserved by interconnection also remains to be done.
Finally, the state/signal framework needs to be tested on more complicated physical
examples. This will surely open up many new interesting questions, which will give
directions for future research.