Fabian Wirth
Dynamics of time-varying discrete-time linear systems: Spectral theory and the projected system
The paper is published: Siam Journal of Control and Optimization, 36(2):447-487, 1998
MSC:
93B05 Controllability
34D08 Lyapunov exponents
Abstract:
We study structural properties of linear time-varying discrete-time
systems. At first an associated system on projective space is
introduced as a basic tool to understand the linear dynamics. We
study controllability properties of this system, and characterize in
particular the control sets and their cores. Sufficient conditions
for an upper bound on the number of control sets with nonempty
interior are given. Furthermore exponential growth rates of the
linear system are studied. Using finite time controllability
properties in the cores of control sets the Floquet spectrum of the
linear system may be described. In particular, the closure of the
Floquet spectrum is contained in the Lyapunov spectrum.


Keywords: Time-varying, discrete-time, control sets, universal controls, projected system, Bohl exponents, Floquet exponents, Lyapunov exponents

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Zentrum für Technomathematik (German)
Institute for Dynamical Systems
The Maths Department
The University of Bremen