On exponential stability for linear discrete-time systems in Banach spaces. (English) Zbl 1247.39014
Summary: We investigate four concepts of exponential stability for difference equations in Banach spaces. Characterizations of these concepts are given. They can be considered as variants for the discrete-time case of the classical results due to E. A. Barbashin [Introduction to stability theory, Nauka, Moscow (1967; Zbl 0155.13501)] and {R. Datko [SIAM J. Math. Anal. 3, 428–445 (1972; Zbl 0241.34071)]. An illustrative example clarifies the relations between these concepts.}
MSC:
| 39A30 | Stability theory for difference equations |
| 39A06 | Linear difference equations |
| 93D20 | Asymptotic stability in control theory |
Keywords:
linear discrete-time systems; uniform exponential stability; (nonuniform) exponential stability; strongly exponential stabilityReferences:
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