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Stabilization of persistently excited linear systems

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.
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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⟩



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