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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Absztrakt (kivonat)

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.

Mű típusa:	Folyóirat
Folyóirat/könyv/kiadvány címe:	Electronic journal of qualitative theory of differential equations
Dátum:	2022
Szám:	19
ISSN:	1417-3875
Nyelv:	angol
Kiadás helye:	Szeged
DOI:	10.14232/ejqtde.2022.1.19
Kulcsszavak:	Differenciálegyenlet
Megjegyzések:	Bibliogr.: p. 30-32. ; összefoglalás angol nyelven
Szakterület:	01. Természettudományok 01. Természettudományok > 01.01. Matematika
Feltöltés dátuma:	2022. máj. 24. 08:57
Utolsó módosítás:	2022. máj. 24. 08:57
URI:	http://acta.bibl.u-szeged.hu/id/eprint/75834

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