Stability results for the functional differential equations associated to water hammer in hydraulics

Răsvan Vladimir: Stability results for the functional differential equations associated to water hammer in hydraulics. (2022)

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Abstract

We consider a system of two sets of partial differential equations describing the water hammer in a hydroelectric power plant containing the dynamics of the tunnel, turbine penstock, surge tank and hydraulic turbine. Under standard simplifying assumptions (negligible Darcy–Weisbach losses and dynamic head variations), a system of functional differential equations of neutral type, with two delays, can be associated to the aforementioned partial differential equations and existence, uniqueness and continuous data dependence can be established. Stability is then discussed using a Lyapunov functional deduced from the energy identity. The Lyapunov functional is “weak” i.e. its derivative function is only non-positive definite. Therefore only Lyapunov stability is obtained while for asymptotic stability application of the Barbashin–Krasovskii–LaSalle invariance principle is required. A necessary condition for its validity is the asymptotic stability of the difference operator associated to the neutral system. However, its properties in the given case make the asymptotic stability non-robust (fragile) in function of some arithmetic properties of the delay ratio.

Item Type: Journal
Publication full: Electronic journal of qualitative theory of differential equations
Date: 2022
Number: 19
ISSN: 1417-3875
Language: English
Place of Publication: Szeged
DOI: 10.14232/ejqtde.2022.1.19
Uncontrolled Keywords: Differenciálegyenlet
Additional Information: Bibliogr.: p. 30-32. ; összefoglalás angol nyelven
Subjects: 01. Natural sciences
01. Natural sciences > 01.01. Mathematics
Date Deposited: 2022. May. 24. 08:57
Last Modified: 2022. May. 24. 08:57
URI: http://acta.bibl.u-szeged.hu/id/eprint/75834

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