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A general transfer function representation for a class of hyperbolic distributed parameter systems

100%

Bartecki K.

International Journal of Applied Mathematics and Computer Science

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2013

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tom 23

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nr 2

291-307

EN

Results of transfer function analysis for a class of distributed parameter systems described by dissipative hyperbolic partial differential equations defined on a one-dimensional spatial domain are presented. For the case of two boundary inputs, the closed-form expressions for the individual elements of the 2×2 transfer function matrix are derived both in the exponential and in the hyperbolic form, based on the decoupled canonical representation of the system. Some important properties of the transfer functions considered are pointed out based on the existing results of semigroup theory. The influence of the location of the boundary inputs on the transfer function representation is demonstrated. The pole-zero as well as frequency response analyses are also performed. The discussion is illustrated with a practical example of a shell and tube heat exchanger operating in parallel- and countercurrent-flow modes.

2

The stability of an irrigation canal system

86%

Bounit H.

International Journal of Applied Mathematics and Computer Science

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2003

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tom 13

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nr 4

453-468

EN

In this paper we examine the stability of an irrigation canal system. The system considered is a single reach of an irrigation canal which is derived from Saint-Venant's equations. It is modelled as a system of nonlinear partial differential equations which is then linearized. The linearized system consists of hyperbolic partial differential equations. Both the control and observation operators are unbounded but admissible. From the theory of symmetric hyperbolic systems, we derive the exponential (or internal) stability of the semigroup underlying the system. Next, we compute explicitly the transfer functions of the system and we show that the input-output (or external) stability holds. Finally, we prove that the system is regular in the sense of (Weiss, 1994) and give various properties related to its transfer functions.

3

J-energy preserving well-posed linear systems

58%

Staffans O. J.

International Journal of Applied Mathematics and Computer Science

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2001

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tom 11

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nr 6

1361-1378

EN

The following is a short survey of the notion of a well-posed linear system. We start by describing the most basic concepts, proceed to discuss dissipative and conservative systems, and finally introduce J-energy-preserving systems, i.e., systems that preserve energy with respect to some generalized inner products (possibly semi-definite or indefinite) in the input, state and output spaces. The class of well-posed linear systems contains most linear time-independent distributed parameter systems: internal or boundary control of PDE’s, integral equations, delay equations, etc. These systems have existed in an implicit form in the mathematics literature for a long time, and they are closely connected to the scattering theory by Lax and Phillips and to the model theory by Sz.-Nagy and Foiaş. The theory has been developed independently by many different schools, and it is only recently that these different approaches have begun to converge. One of the most interesting objects of the present study is the Riccati equation theory for this class of infinite-dimensional systems (H^2 - and H^∞ -theories).

Ograniczanie wyników

3 International Journal of Applied Mathematics and Computer Science

1 Bartecki K.

1 Bounit H.

1 Staffans O. J.

1 2013

1 2003

1 2001

A general transfer function representation for a class of hyperbolic distributed parameter systems

The stability of an irrigation canal system

J-energy preserving well-posed linear systems