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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Submitted on : Tuesday, September 6, 2016 - 11:35:38 AM
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Dan Goreac, Claudia Grosu, Eduard Rotenstein. Approximate and Approximate Null-Controllability of a Class of Piecewise Linear Markov Switch Systems. Systems and Control Letters, Elsevier, 2016, 96, pp.118-123. ⟨http://www.sciencedirect.com/science/article/pii/S0167691116300998⟩. ⟨10.1016/j.sysconle.2016.07.003⟩. ⟨hal-01266268v2⟩

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