Stability of Difference Equations and Applications to Robustness Problems

• Main Author: Sasu Bogdan
• Format: Article
• Language: English
• Published: SpringerOpen 2010-01-01
• Series: Advances in Difference Equations
• Online Access: http://www.advancesindifferenceequations.com/content/2010/869608

<p/> <p>The aim of this paper is to obtain new necessary and sufficient conditions for the uniform exponential stability of variational difference equations with applications to robustness problems. We prove characterizations for exponential stability of variational difference equations using translation invariant sequence spaces and emphasize the importance of each hypothesis. We introduce a new concept of stability radius <inline-formula><graphic file="1687-1847-2010-869608-i1.gif"/></inline-formula><inline-formula><graphic file="1687-1847-2010-869608-i2.gif"/></inline-formula> for a variational system of difference equations <inline-formula><graphic file="1687-1847-2010-869608-i3.gif"/></inline-formula> with respect to a perturbation structure <inline-formula><graphic file="1687-1847-2010-869608-i4.gif"/></inline-formula> and deduce a very general estimate for the lower bound of <inline-formula><graphic file="1687-1847-2010-869608-i5.gif"/></inline-formula><inline-formula><graphic file="1687-1847-2010-869608-i6.gif"/></inline-formula>. All the results are obtained without any restriction concerning the coefficients, being applicable for any system of variational difference equations.</p>