Abstract:
In the study of the joint spectral radius
of linear operators, an important role is played
by invariant norms and
invariant convex bodies.
It is known that they are dual to each other in the sense of the polar transform
and conjugation of operators.
This property is used in studying the highest growth rate of trajectories of
discrete-time
linear dynamical systems.
In the case of continuous-time systems, an analog of joint spectral radius is
Lyapunov exponent.
For such systems,
invariant norms have been defined and their existence has been proved.
However, there are no results concerning the invariant bodies of
continuous-time systems in the literature.
This paper is devoted to the duality of continuous-time systems.
It is shown that there exists no natural notion of an
invariant body for such systems and, therefore, the duality of systems is defined in
terms of invariant norms.
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