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ISSN 0012-2661, Differential Equations, 2007, Vol. 43, No. 1, pp. 43–55. c Pleiades Publishing, Ltd., 2007. Original Russian Text c V.M. Marchenko, J.-J. Loiseau, 2007, published in Differentsial’nye Uravneniya, 2007, Vol. 43, No. 1, pp. 41–51. ORDINARY DIFFERENTIAL EQUATIONS Realization of Dynamical Systems in Scales of Systems with Aftereffect: II. Controllability. Observability. Minimality V. M. Marchenko and J.-J. Loiseau Bialystok Technical University, Bialystok, Poland Belarus State Technological University, Minsk, Belarus Institut de Recherche en Communications et Cybern´ etique de Nantes (IRCCyN), Central School, Nantes, France Received June 28, 2006 DOI: 10.1134/S0012266107010077 INTRODUCTION The present paper directly continues the studies [1] of the realization of transfer functions in scales of dynamical systems with retarded argument. The notation introduced in [1] is used throughout the following without special notice unless misunderstanding can occur. Below we mainly focus our attention on the following classes of dynamical systems with retarded argument: the simplest delay system x ˙ (t)= Ax(t)+ A x(t − h)+ Bu(t),y(t)= Cx(t),t> 0, (0.1) and the system with many delays with respect to the state, control, and output (the multiple delay system) l l x ˙ (t)= (A x(t − jh)+ B u(t − jh)),y(t)= C x(t −
Differential Equations – Springer Journals
Published: Feb 24, 2007
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