Floquet theory based on new periodicity concept for hybrid systems involving q-difference equations

Using the new periodicity concept based on shifts, we construct a unified Floquet theory for homogeneous and nonhomogeneous hybrid periodic systems on domains having continuous, discrete or hybrid structure. New periodicity concept based on shifts enables the construction of Floquet theory on hybrid...

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Bibliographic Details
Published in:Applied mathematics and computation 2016-01, Vol.273, p.1208-1233
Main Authors: Adıvar, Murat, Koyuncuoğlu, Halis Can
Format: Article
Language:English
Subjects:
Floquet
Hybrid system
Lyapunov
Periodicity
Shift operators
Stability
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Summary:Using the new periodicity concept based on shifts, we construct a unified Floquet theory for homogeneous and nonhomogeneous hybrid periodic systems on domains having continuous, discrete or hybrid structure. New periodicity concept based on shifts enables the construction of Floquet theory on hybrid domains that are not necessarily additive periodic. This makes periodicity and stability analysis of hybrid periodic systems possible on non-additive domains. In particular, this new approach can be useful to know more about Floquet theory for linear q-difference systems defined on qZ¯:={qn:n∈Z}∪{0} where q > 1. By constructing the solution of matrix exponential equation we establish a canonical Floquet decomposition theorem. Determining the relation between Floquet multipliers and Floquet exponents, we give a spectral mapping theorem on closed subsets of reals that are periodic in shifts. Finally, we show how the constructed theory can be utilized for the stability analysis of dynamic systems on periodic time scales in shifts.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2015.08.124