On the perturbations preserving spectrum of discrete linear systems

Abstract

This paper focuses on the issue of description of the set of parametric perturbation which preserves the spectrum of a discrete linear time varying system. We prove that all perturbations with the Lyapunov exponent lower then a regularity coefficient are characterized with this feature. Moreover, in case of a diagonal system, the perturbations with Lyapunov exponent equal to the regularity coefficient also reveal this feature.

Keywords:

• characteristic exponents
• time-varying linear systems
• perturbation
• Lyapunov exponent

Acknowledgements

The research presented here were done as a part of research and development project no. O R00 0021 06 and have been supported by Ministry of Science and Higher Education funds in the years 2008–2010.