# 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}
}
• Published 25 November 2021
• Mathematics
• Journal of Dynamical and Control Systems
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…

## References

SHOWING 1-10 OF 30 REFERENCES
On the Fattorini criterion for approximate controllability and stabilizability of parabolic systems
• Mathematics
• 2014
In this paper, we consider the well-known Fattorini's criterion for approximate controllability of infinite dimensional linear systems of type $y'=A y+Bu$. We precise the result proved by H. O.
Controllability of the one-dimensional fractional heat equation under positivity constraints
• Mathematics
• 2019
In this paper, we analyze the controllability properties under positivity constraints on the control or the state of a one-dimensional heat equation involving the fractional Laplacian $(-\Delta)^s$
Control and Nonlinearity
This book presents methods to study the controllability and the stabilization of nonlinear control systems in finite and infinite dimensions. The emphasis is put on specific phenomena due to
Controllability of 2D Euler and Navier-Stokes Equations by Degenerate Forcing
• Mathematics
• 2005
AbstractWe study controllability issues for the 2D Euler and Navier-Stokes (NS) systems under periodic boundary conditions. These systems describe the motion of the homogeneous ideal or viscous
A Pursuit Problem in an Infinite System of Second-Order Differential Equations
• Mathematics
• 2014
We study a pursuit differential game problem for an infinite system of second-order differential equations. The control functions of players, i.e., a pursuer and an evader are subject to integral
On game problems for second-order evolution equations
• Mathematics
• 2007
1. In this paper, we consider certain problems of the theory of differential games in systems with distributed parameters. The players influence on the systemwith the use of control parameters