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Exact observability and controllability for linear neutral type systems
Affiliation:1. IRCCyN/École des Mines, 4 rue Alfred Kastler, BP 20722, 44307 Nantes, France;2. Inst. of Math., University of Szczecin, Wielkopolska 15, 70451 Szczecin, Poland;1. Université Paris-Est, LAMA (UMR 8050), UPEMLV, UPEC, CNRS, F-77454, Marne-la-Vallée, France;2. Faculty of Mathematics, “Alexandru Ioan Cuza” University, Bd. Carol I, no. 9-11, Iasi, Romania;1. Thales Services, 3 avenue de l׳Europe, 31400 Toulouse, France;2. Institut de Mécanique Céleste et de Calcul des Éphémérides (IMCCE), 77 Avenue Denfert Rochereau, 75014 Paris, France;3. ENSTA Paristech, Laboratoire de Mathématiques Appliquées, 828 Boulevard des Maréchaux, 91762 Palaiseau Cedex, France;1. Department of Psychiatry, Pomeranian Medical University, Szczecin, Poland;2. Department of Pharmacology, Institute of Psychiatry and Neurology, Warszawa, Poland;3. Dialogue Therapy Centre, Warszawa, Poland;4. Institute of Psychology, Department of Clinical Psychology, University of Szczecin, Szczecin, Poland;1. Institut de Recherche en Génie Civil et Mécanique (GeM, UMR 6183 CNRS), École Centrale Nantes, 1 rue de la Noë, BP 92101, F-44321 Nantes, France;2. Institute of Mechanics, Materials and Civil Engineering (iMMC), Université catholique de Louvain, 4 ave. G. Lemaître, B-1348 Louvain-la-Neuve, Belgium
Abstract:The problem of exact observability is analyzed for a wide class of neutral type systems by an infinite dimensional approach. The duality with the exact controllability problem is the main tool. It is based on an explicit expression of a neutral type system which corresponding to the abstract adjoint system. A nontrivial relation is obtained between the initial neutral system and the system obtained via the adjoint abstract state operator. The characterization of the duality between controllability and observability is deduced, and then observability conditions are obtained.
Keywords:Observability  Controllability  Duality  Neutral type systems
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