Stabilization of persistently excited linear systems

Yacine Chitour 1, 2 Guilherme Mazanti 1 Mario Sigalotti 1, 3
1 GECO - Geometric Control Design
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France
2 Division Systèmes - L2S
L2S - Laboratoire des signaux et systèmes : 1289
Abstract : This chapter presents recent developments on the stabilization of persistently excited linear systems. The first section of the chapter deals with finite-dimensional systems and gives two main results on stabilization, concerning neutrally stable systems and systems whose eigenvalues all have non-positive real parts. It also presents a result stating the existence of persistently excited systems for which the pair (A, b) is controllable but that cannot be stabilized by means of a linear state feedback. The second section presents some results for infinite-dimensional systems to the case of systems defined by a linear operator A which generates a strongly continuous contraction semigroup, with applications to Schrödinger's equation and the wave equation. The final section discusses some problems that remain open, giving some preliminary results in certain cases.
Document type :
Book sections
Complete list of metadatas
Contributor : Mario Sigalotti <>
Submitted on : Friday, January 3, 2014 - 4:11:28 PM
Last modification on : Thursday, December 5, 2019 - 5:18:51 PM

Links full text



Yacine Chitour, Guilherme Mazanti, Mario Sigalotti. Stabilization of persistently excited linear systems. Jamal Daafouz and Sophie Tarbouriech and Mario Sigalotti. Hybrid Systems with Constraints, Wiley-ISTE, pp.85-120, 2013, 978-1-84821-527-6. ⟨10.1002/9781118639856.ch4 ⟩. ⟨hal-00923619⟩



Record views