Control and stabilization of 2 × 2 hyperbolic systems on graphs | Zendy

Serge Nicaise | Zendy

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Control and stabilization of 2 × 2 hyperbolic systems on graphs

Author(s) -

Serge Nicaise

Publication year - 2016

Publication title -

mathematical control and related fields

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.658

H-Index - 21

eISSN - 2156-8472

pISSN - 2156-8499

DOI - 10.3934/mcrf.2017004

Subject(s) - observability , controllability , dissipative system , mathematics , perturbation (astronomy) , converse , boundary (topology) , mathematical analysis , control theory (sociology) , control (management) , physics , computer science , quantum mechanics , geometry , artificial intelligence

We consider 2× 2 (first order) hyperbolic systems on networks subject to general transmission conditions and to some dissipative boundary conditions on some external vertices. We find sufficient but natural conditions on these transmission conditions that guarantee the exponential decay of the full system on graphs with dissipative conditions at all except one external vertices. This result is obtained with the help of a perturbation argument and an observability estimate for an associated wave type equation. An exact controllability result is also deduced.

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