On the existence of an optimal solution of the Mayer problem governed by 2D continuous counterpart of the Fornasini-Marchesini model

Bors, Dorota; Majewski, Marek

doi:10.1007/s11045-012-0207-2

Cited by 3 publications

(2 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We note that continuous-time counterparts of Fornasini-Marchesini models of a somewhat different form have been considered in the literature (see [23] and the references there).…”

Section: Triple Of Operators Such Thatmentioning

confidence: 99%

Schur–Agler and Herglotz–Agler classes of functions: Positive-kernel decompositions and transfer-function realizations

Ball

Kaliuzhnyi-Verbovetskyi

2015

Advances in Mathematics

View full text Add to dashboard Cite

Abstract. We discuss transfer-function realization for multivariable holomorphic functions mapping the unit polydisk or the right polyhalfplane into the operator analogue of either the unit disk or the right halfplane (Schur/Herglotz functions over either the unit polydisk or the right polyhalfplane) which satisfy the appropriate stronger contractive/positive real part condition for the values of these functions on commutative tuples of strict contractions/strictly accretive operators (Schur-Agler/Herglotz-Agler functions over either the unit polydisk or the right polyhalfplane). As originally shown by Agler, the first case (polydisk to disk) can be solved via unitary extensions of a partially defined isometry constructed in a canonical way from a kernel decomposition for the function (the lurking-isometry method). We show how a geometric reformulation of the lurking-isometry method (embedding of a given isotropic subspace of a Kreȋn space into a Lagrangian subspace-the lurking-isotropicsubspace method) can be used to handle the second two cases (polydisk to halfplane and polyhalfplane to disk), as well as the last case (polyhalfplane to halfplane) if an additional growth condition at ∞ is imposed. For the general fourth case, we show how a linear-fractional-transformation change of variable can be used to arrive at the appropriate symmetrized nonhomogeneous Bessmertnyȋ long-resolvent realization. We also indicate how this last result recovers the classical integral representation formula for scalar-valued holomorphic functions mapping the right halfplane into itself.

show abstract

“…We note that continuous-time counterparts of Fornasini-Marchesini models of a somewhat different form have been considered in the literature (see [23] and the references there).…”

Section: Triple Of Operators Such Thatmentioning

confidence: 99%

Schur–Agler and Herglotz–Agler classes of functions: Positive-kernel decompositions and transfer-function realizations

Ball

Kaliuzhnyi-Verbovetskyi

2015

Advances in Mathematics

View full text Add to dashboard Cite

show abstract

“…For discrete two-dimensional (2D) systems, the most popular are the structures of the state-space models proposed by Roesser [4], Fornasini and Marchesini [5,6], and Kurek [7]. These models are also adopted for continuous domain in [8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

General Response Formula for CFD Pseudo-Fractional 2D Continuous Linear Systems Described by the Roesser Model

Rogowski

2020

Symmetry

View full text Add to dashboard Cite

In many engineering problems associated with various physical phenomena, there occurs a necessity of analysis of signals that are described by multidimensional functions of more than one variable such as time t or space coordinates x, y, z. Therefore, in such cases, we should consider dynamical models of two or more dimensions. In this paper, a new two-dimensional (2D) model described by the Roesser type of state-space equations will be considered. In the introduced model, partial differential operators described by the Conformable Fractional Derivative (CFD) definition with respect to the first (horizontal) and second (vertical) variables will be applied. For the model under consideration, the general response formula is derived using the inverse fractional Laplace method. Next, the properties of the solution will be considered. Usefulness of the general response formula will be discussed and illustrated by a numerical example.

show abstract

Nonlinear continuous Fornasini–Marchesini model of fractional order with nonzero initial conditions

Idczak¹,

Kamocki²,

Majewski³

2020

J. Integral Equations Applications

View full text Add to dashboard Cite

On the existence of an optimal solution of the Mayer problem governed by 2D continuous counterpart of the Fornasini-Marchesini model

Cited by 3 publications

References 14 publications

Schur–Agler and Herglotz–Agler classes of functions: Positive-kernel decompositions and transfer-function realizations

Schur–Agler and Herglotz–Agler classes of functions: Positive-kernel decompositions and transfer-function realizations

General Response Formula for CFD Pseudo-Fractional 2D Continuous Linear Systems Described by the Roesser Model

Nonlinear continuous Fornasini–Marchesini model of fractional order with nonzero initial conditions

Contact Info

Product

Resources

About