Preprint 16-2014

Stability analysis of implicit difference equations under restricted perturbations

Author(s) : Volker Mehrmann , Do-Duc Thuan

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 16-2014

MSC 2000

47A10 Spectrum, resolvent

34D99 None of the above, but in this section

Abstract :
The stability analysis for linear implicit m-th order difference equations is discussed. We allow the leading coefficient coefficient to be singular, i.e., we include the situation that the system does not generate an explicit recursion. A spectral condition for the characterization of asymptotic stability is presented and computable formulas are derived for the real and complex stability radii in the case that the coefficient matrices are subjected to structured perturbations.

Keywords : Implicit difference equation, asymptotic stability, structured perturbation, stability radius, strangeness-free system, positive system