On the Stability and Null-Controllability of an Infinite System of Linear Differential Equations
Keyword(s):
AbstractIn 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 dependence of the stability on the norm, i.e. the same system considered $\ell ^{\infty }$ ℓ ∞ is not asymptotically stable if λ = − 1.
2011 ◽
Vol 2011
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pp. 1-15
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2017 ◽
Vol 36
(2)
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pp. 485-513
2017 ◽
Vol 24
(12)
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pp. 2656-2670
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1975 ◽
Vol 27
(3)
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pp. 691-703
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2002 ◽
Vol 29
(3)
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pp. 155-166
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