# The stability of an irrigation canal system

• Volume: 13, Issue: 4, page 453-468
• ISSN: 1641-876X

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## Abstract

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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.

## How to cite

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Bounit, Hamid. "The stability of an irrigation canal system." International Journal of Applied Mathematics and Computer Science 13.4 (2003): 453-468. <http://eudml.org/doc/207657>.

@article{Bounit2003,
abstract = {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.},
author = {Bounit, Hamid},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {transfer function; Saint-Venant equation; input-output stability; regular systems; symmetric hyperbolic equation; internal stability; dimensionless; dimensionless symmetric hyperbolic equation},
language = {eng},
number = {4},
pages = {453-468},
title = {The stability of an irrigation canal system},
url = {http://eudml.org/doc/207657},
volume = {13},
year = {2003},
}

TY - JOUR
AU - Bounit, Hamid
TI - The stability of an irrigation canal system
JO - International Journal of Applied Mathematics and Computer Science
PY - 2003
VL - 13
IS - 4
SP - 453
EP - 468
AB - 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.
LA - eng
KW - transfer function; Saint-Venant equation; input-output stability; regular systems; symmetric hyperbolic equation; internal stability; dimensionless; dimensionless symmetric hyperbolic equation
UR - http://eudml.org/doc/207657
ER -

## References

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