On exponential stability for linear discrete-time systems in Banach spaces

In this paper 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 [2] and R. Datko [5]. An illustrative example clarifies the relations between these concepts.Comment: Computers & Mathematics with Applications, accepted for publicatio

On Barreira-Valls polynomial stability of evolution operators in Banach spaces

Our main objective is to consider a concept of nonuniform behavior and obtain appropriate versions of the well-known stability due to R. Datko and L. Barbashin. This concept has been considered in the works of L. Barreira and C. Valls. Our approach is based on the extension of techniques for exponential stability to the case of polynomial stability

Uniform exponential trisplitting – a new criterion for discrete skew-product semiflows

In the present paper the concept of uniform exponential trisplitting for skew-product flows in Banach space is considered. This concept is a generalisation of the well-known concept of uniform exponential trichotomy. Connections between these concepts are presented and some illustrating examples prove that these are distinct. Also, we present necessary and sufficient conditions for the uniform exponential trisplitting concept with invariant and strongly invariant projectors. Finally, a characterisation in terms of Lyapunov sequences is given

Uniform exponential trisplitting – a new criterion for discrete skew-product semiflows

In the present paper the concept of uniform exponential trisplitting for skew-product flows in Banach space is considered. This concept is a generalisation of the well-known concept of uniform exponential trichotomy. Connections between these concepts are presented and some illustrating examples prove that these are distinct. Also, we present necessary and sufficient conditions for the uniform exponential trisplitting concept with invariant and strongly invariant projectors. Finally, a characterisation in terms of Lyapunov sequences is given