Fabian Wirth
On stability of infinite-dimensional discrete inclusions
The paper is published: Summary in Journal of Mathematical Systems, Estimation, and Control. 8(4):507-510, 1998, Full electronic manuscript, 21 pp. 429 KB, Retrieval code 72701, ftp://trick.ntp.springer.de/pub/jmsec/
MSC:
34D08 Lyapunov exponents
93D09 Robust stability
Abstract:
For discrete inclusions in Banach spaces we study
stability questions. First it is shown that the Bohl exponent of a
time-varying discrete time system can be characterized via the
spectral radius of an associated operator on the space of p-th
order summable sequences. The main result is that for discrete
inclusions on a reflexive Banach space various characteristic
exponents characterizing different concepts of stability coincide.
Using this result it is shown that the convexification of an
exponentially stable discrete inclusions is exponentially stable.
It is examined to what extent these results can be carried over to
the time-varying case.


Keywords: Discrete inclusion, time-varying, infinite dimensional, Bohl exponents, Lyapunov exponents, stability