Fabian Wirth, Diederich Hinrichsen
Exponential stability of families of linear delay systems.
Preprint series: Proceedings of the Symposium on Mathematical Theory of Networks and Systems MTNS-2000, Perpignan, France, 2000
93D09 Robust stability
34K20 Stability theory
We analyze exponential stability concepts for families of linear
delay systems. The main result states that for such families with
coefficients varying in compact convex sets various characteristic
exponents characterizing different concepts of stability coincide.
This result is obtained using methods from the theory of discrete
inclusions in Banach spaces. As a further application of this
approach a new result on slowly-varying discrete inclusions is
applied to the delay equation setting. This shows that just as in
the standard case of time-varying systems the exponential behavior
of a slowly time-varying system is determined by the limit family.

Keywords: Stability, delay systems, infinite dimensional system, discrete inclusions