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… 

References

SHOWING 1-10 OF 30 REFERENCES
On the Fattorini criterion for approximate controllability and stabilizability of parabolic systems
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.
Decomposition and suboptimal control in dynamical systems
Optimal linear-quadratic control of asymptotically stabilizable systems using approximations
Controllability of the one-dimensional fractional heat equation under positivity constraints
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
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
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
Bounded controls in distributed-parameter systems
On game problems for second-order evolution equations
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
...
1
2
3
...