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2020 Characterization by observability inequalities of controllability and stabilization properties
Emmanuel Trélat, Gengsheng Wang, Yashan Xu
Pure Appl. Anal. 2(1): 93-122 (2020). DOI: 10.2140/paa.2020.2.93

Abstract

Given a linear control system in a Hilbert space with a bounded control operator, we establish a characterization of exponential stabilizability in terms of an observability inequality. Such dual characterizations are well known for exact (null) controllability. Our approach exploits classical Fenchel duality arguments and, in turn, leads to characterizations in terms of observability inequalities of approximate null controllability and of α-null controllability. We comment on the relationships among those various concepts, at the light of the observability inequalities that characterize them.

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Emmanuel Trélat. Gengsheng Wang. Yashan Xu. "Characterization by observability inequalities of controllability and stabilization properties." Pure Appl. Anal. 2 (1) 93 - 122, 2020. https://doi.org/10.2140/paa.2020.2.93

Information

Received: 30 April 2019; Revised: 19 June 2019; Accepted: 22 July 2019; Published: 2020
First available in Project Euclid: 13 December 2019

zbMATH: 07159298
MathSciNet: MR4041279
Digital Object Identifier: 10.2140/paa.2020.2.93

Subjects:
Primary: 93B05 , 93B07 , 93C20

Keywords: Controllability , observability inequality , stabilizability

Rights: Copyright © 2020 Mathematical Sciences Publishers

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