Approximate and Approximate Null-Controllability of a Class of Piecewise Linear Markov Switch Systems

Dan Goreac 1 Claudia Grosu 2 Eduard Rotenstein 2
1 PS
LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
Abstract : We propose an explicit, easily-computable algebraic criterion for approximate null-controllability of a class of general piecewise linear switch systems with multiplicative noise. This gives an answer to the general problem left open in [13]. The proof relies on recent results in [4] allowing to reduce the dual stochastic backward system to a family of ordinary differential equations. Second, we prove by examples that the notion of approximate controllability is strictly stronger than approximate null-controllability. A sufficient criterion for this stronger notion is also provided. The results are illustrated on a model derived from repressed bacterium operon (given in [19] and reduced in [5]).
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https://hal-upec-upem.archives-ouvertes.fr/hal-01266268
Contributor : Dan Goreac <>
Submitted on : Tuesday, February 2, 2016 - 1:11:17 PM
Last modification on : Wednesday, September 4, 2019 - 1:52:20 PM
Long-term archiving on: Saturday, November 12, 2016 - 2:31:47 AM

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  • HAL Id : hal-01266268, version 1
  • ARXIV : 1602.00920

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Dan Goreac, Claudia Grosu, Eduard Rotenstein. Approximate and Approximate Null-Controllability of a Class of Piecewise Linear Markov Switch Systems. 2016. ⟨hal-01266268v1⟩

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