Global internal stabilizability does not imply global external stabilizability for small sensor disturbances

R. Freeman

doi:10.1109/9.478336

Global internal stabilizability does not imply global external stabilizability for small sensor disturbances

IEEE Transactions on Automatic Control ◽

10.1109/9.478336 ◽

1995 ◽

Vol 40 (12) ◽

pp. 2119-2122 ◽

Cited By ~ 62

Author(s):

R. Freeman

Keyword(s):

Internal Stabilizability

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Stabilizing A Reaction-Diffusion System Via Feedback Control

Annals of the Alexandru Ioan Cuza University - Mathematics ◽

10.2478/v10157-012-0032-9 ◽

2013 ◽

Vol 59 (1) ◽

pp. 191-200

Author(s):

Smaranda C. Dodea

Keyword(s):

Feedback Control ◽

Principal Eigenvalue ◽

Reaction Diffusion ◽

Reaction Diffusion System ◽

Diffusion System ◽

Necessary Condition ◽

System Modelling ◽

Stabilizing Control ◽

Internal Stabilizability ◽

Predator System

Abstract A two-component reaction-diffusion system modelling a prey-predator system is considered. A necessary condition and a sufficient condition for the internal stabilizability to zero of one the two components of the solution while preserving the nonnegativity of both components have been established by Aniţa. In case of stabilizability, a feedback stabilizing control of harvesting type has been indicated. The rate of stabilization corresponding to the indicated feedback control depends on the principal eigenvalue of a certain elliptic operator. A large principal eigenvalue leads to a fast stabilization. The first goal of this paper is to approximate this principal eigenvalue. The second goal is to derive a conceptual iterative algorithm to improve at each iteration the position of the support of the stabilizing control in order to get a faster stabilization.

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