Stability by the linear approximation for discrete equations

作者：Czornik Adam^*; Nawrat Aleksander

来源：Linear Algebra and Its Applications, 2011, 435(4): 742-750.

DOI：10.1016/j.laa.2011.02.020

• Difference equation
• Stability
• Time-varying systems
• Lyapunov exponents
• Linearization

This paper is concerned with exponential stability of solutions of perturbed discrete equations. For a given m > 1 we will provide necessary and sufficient conditions for exponential stability of all perturbed systems with perturbation of order m under the assumption that the unperturbed linear system is exponentially stable. Basing on this result we obtained necessary and sufficient conditions for exponential stability of the perturbed system for all perturbations of order m > 1 for regular systems. Our results are expressed in terms of regular coefficients of the unperturbed system.

• 出版日期2011-8-15