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March  2019, 9(1): 39-58. doi: 10.3934/mcrf.2019002

## Decay rates for stabilization of linear continuous-time systems with random switching

 1 Institut für Mathematik, Universität Augsburg, 86159 Augsburg, Germany 2 Laboratoire de Mathématiques d'Orsay, Univ. Paris-Sud, Université Paris-Saclay, 91405 Orsay, France

* Corresponding author: Guilherme Mazanti

Received  May 2017 Revised  March 2018 Published  August 2018

Fund Project: The first author is supported by DFG grant Co 124/19-1. The second author is partially supported by the iCODE Institute, research project of the IDEX Paris-Saclay, and by the Hadamard Mathematics LabEx (LMH) through the grant number ANR-11-LABX-0056-LMH in the "Programme des Investissements d'Avenir". This work was prepared while the second author was with CMAP & Inria, team GECO, École Polytechnique, CNRS, Université Paris-Saclay, 91128 Palaiseau Cedex, France.

For a class of linear switched systems in continuous time a controllability condition implies that state feedbacks allow to achieve almost sure stabilization with arbitrary exponential decay rates. This is based on the Multiplicative Ergodic Theorem applied to an associated system in discrete time. This result is related to the stabilizability problem for linear persistently excited systems.

Citation: Fritz Colonius, Guilherme Mazanti. Decay rates for stabilization of linear continuous-time systems with random switching. Mathematical Control & Related Fields, 2019, 9 (1) : 39-58. doi: 10.3934/mcrf.2019002
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