Constrained asymptotic null-controllability for semi-linear infinite dimensional systems

2020 ◽  
Author(s):  
Lahoucine Boujallal ◽  
Khalid Kassara
Keyword(s):  
Null Controllability ◽  
Infinite Dimensional ◽  
Infinite Dimensional Systems

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

2021 ◽  
Author(s):  
Abdulla Azamov ◽  
Gafurjan Ibragimov ◽  
Khudoyor Mamayusupov ◽  
Marks Ruziboev
Keyword(s):  
Infinite System ◽  
Null Controllability ◽  
Infinite Matrix ◽  
Asymptotically Stable ◽  
Controllability Problem ◽  
Infinite Dimensional ◽  
Infinite Dimensional Systems ◽  
The Matrix ◽  
Linear Differential ◽  
The Stability

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.

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