State-space realization theory of two-dimensional filters

Fornasini, Ettore; Marchesini, G.

doi:10.1109/tac.1976.1101305

Cited by 608 publications

(237 citation statements)

References 8 publications

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“…It should be underlined that such discrete systems play an important role in the theory of automatic control (cf. Fornasini and Marchesini 1976). Moreover, continuous systems of the form specified by (1) can be used for modelling of the process of gas absorption (cf.…”

Section: F T ϕ (T) ϕ (T) ψ (T) ψ (T) Dt + G ϕ (0) ϕ (0) ψ mentioning

confidence: 99%

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

Bors

Majewski

2012

Multidim Syst Sign Process

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In the paper the optimization problem described by some nonlinear hyperbolic equation being continuous counterpart of the Fornasini-Marchesini model is considered. A theorem on the existence of at least one solution to this hyperbolic PDE is proved and some properties of the set of all solutions are established. The existence of a solution to an optimization problem under appropriate assumptions is the main result of this paper. Some application of the obtained results to the process of gas filtration is also presented.Keywords Mayer problem · Continuous counterpart of the Fornasini-Marchesini model · Existence of optimal solutions

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Section: F T ϕ (T) ϕ (T) ψ (T) ψ (T) Dt + G ϕ (0) ϕ (0) ψ mentioning

confidence: 99%

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

Bors

Majewski

2012

Multidim Syst Sign Process

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“…The most popular models of two-dimensional (2D) linear systems are the models introduced in [1][2][3] and [4]. These models have been extended for positive systems in [5][6][7][8].…”

Section: Introductionmentioning

confidence: 99%

Positivity and stability of fractional 2D Lyapunov systems described by the Roesser model

Rogowski¹

2011

Bulletin of the Polish Academy of Sciences: Technical Sciences

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Abstract.A new class of fractional 2D Lyapunov systems described by the Roesser models is introduced. Necessary and sufficient conditions for the positivity and asymptotic stability of the new class of systems are established. It is shown that the checking of the asymptotic stability of positive 2D fractional Lyapunov systems can be reduced to testing the asymptotic stability of corresponding positive standard 1D discretetime systems. The considerations are illustrated by a numerical example.

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“…The most popular models of two-dimensional (2D) linear systems are the ones introduced by Roesser (1975), Fornasini-Marchesini (1976;1978) and Kurek (1985). These models were extended to positive systems in (Valcher, 1997;Kaczorek, 1996;2005).…”

Section: Introductionmentioning

confidence: 99%

Positivity and stabilization of fractional 2D linear systems described by the Roesser model

Kaczorek¹,

Rogowski²

2010

International Journal of Applied Mathematics and Computer Science

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A new class of fractional 2D linear discrete-time systems is introduced. The fractional difference definition is applied to each dimension of a 2D Roesser model. Solutions of these systems are derived using a 2D Z-transform. The classical Cayley-Hamilton theorem is extended to 2D fractional systems described by the Roesser model. Necessary and sufficient conditions for the positivity and stabilization by the state-feedback of fractional 2D linear systems are established. A procedure for the computation of a gain matrix is proposed and illustrated by a numerical example.

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State-space realization theory of two-dimensional filters

Cited by 608 publications

References 8 publications

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

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

Positivity and stability of fractional 2D Lyapunov systems described by the Roesser model

Positivity and stabilization of fractional 2D linear systems described by the Roesser model

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