# On the Stability and Null-Controllability of an Infinite System of Linear Differential Equations

@article{Azamov2021OnTS, title={On the Stability and Null-Controllability of an Infinite System of Linear Differential Equations}, author={Abdulla A. Azamov and Gafurjan I. Ibragimov and Khudoyor Mamayusupov and Marks Ruziboev}, journal={Journal of Dynamical and Control Systems}, year={2021} }

In this work, the null controllability problem for a linear system in ℓ2 is considered, where the matrix of a linear operator describing the system is an infinite matrix with $\lambda \in \mathbb {R}$
λ
∈
ℝ
on the main diagonal and 1s above it. We show that the system is asymptotically stable if and only if λ ≤− 1, which shows the fine difference between the finite and the infinite-dimensional systems. When λ ≤− 1 we also show that the system is null controllable in large. Further we show a…

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