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Exponential and weak stabilization for distributed bilinear systems with time delay via bounded feedback control
Author(s) -
Tsouli Azzeddine,
El Houch Atmane
Publication year - 2021
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.2254
Subject(s) - observability , bounded function , hilbert space , mathematics , control theory (sociology) , compact space , exponential stability , operator (biology) , exponential growth , distributed parameter system , bilinear interpolation , bounded operator , control (management) , partial differential equation , mathematical analysis , nonlinear system , computer science , biochemistry , chemistry , physics , repressor , quantum mechanics , artificial intelligence , transcription factor , gene , statistics
In this paper, we deal with the problem of exponential and weak stabilization for a class of distributed bilinear systems with time delay in a Hilbert space by using bounded feedback control. In the case of exponential stabilization, an explicit decay rate estimate of the stabilized state is given provided that a non‐standard observability inequality condition is satisfied. The compactness hypothesis of the control operator prevents the validity of the non‐standard observability inequality, thus it can be relaxed to a weaker sufficient condition to show the weak stabilization result by employing the same feedback control. Finally, numerical examples and simulations to hyperbolic and parabolic partial functional differential equations are considered to illustrate the effectiveness of the obtained theoretical results.