# The stability of an irrigation canal system

International Journal of Applied Mathematics and Computer Science (2003)

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

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topBounit, 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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