On the Lyapunov exponents of a class of second-order discrete time linear systems with bounded perturbations

Abstract

In this note we describe the maximal and the minimal values of Lyapunov exponents for second-order discrete time-invariant linear system perturbed by time-varying bounded perturbations. An interpretation of the results in terms of generalized spectral radius is given. An application of obtained formulas to the robust stability problem is demonstrated on a numerical example.

Keywords:

• time-varying discrete linear systems
• Lyapunov exponents
• robust stability
• generalized spectral radius

Acknowledgements

The research presented here were supported by the Ministry of Science and Higher Education funds BK/233/RAU1/2012 and co-financed by European Union within European Social Fund within SWIFT project POKL. 08.02.01-24-005/10.