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Discrete admissibility and exponential trichotomy of dynamical systems. (English) Zbl 1302.39027

The goal of the paper is to study the uniform exponential trichotomy of the difference equation \(x(n+1)=A(n)x(n)\) in terms of the solvability of the input-output system \(\gamma (n+1) = A(n)\gamma (n)+s(n+1)\). The main results are Perron-type theorems. Some applications for evolution families are given.

MSC:

39A30 Stability theory for difference equations
93C55 Discrete-time control/observation systems
93D25 Input-output approaches in control theory
39A10 Additive difference equations
39A12 Discrete version of topics in analysis
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