Stability of fractional order time delay systems
Апстракт
In this paper, some basic results of the stability criteria of fractional order system
with time delay as well as free delay are presented. Also, they are obtained and presented
sufficient conditions for finite time stability for (non)linear (non)homogeneous as well as
perturbed fractional order time delay systems. Several stability criteria for this class of
fractional order systems are proposed using a recently suggested generalized Gronwall
inequality as well as “classical” Bellman-Gronwall inequality. Some conclusions for
stability are similar to that of classical integer-order differential equations. Last, a numerical
example is given to illustrate the validity of the proposed procedure.
Кључне речи:
finite-time stability / fractional order / Time delayed systemsИзвор:
Proceedings of the 3rd International Congress of Serbian Society of Mechanics (IConSSM 2011),Vlasina lake (Serbia), 5-8 July 2011, 2011, 44-69Издавач:
- Belgrade: Serbian Society of Mechanics
Финансирање / пројекти:
- Одрживост и унапређење машинских система у енергетици и транспорту применом форензичког инжењерства, еко и робуст дизајна (RS-MESTD-Technological Development (TD or TR)-35006)
Колекције
Институција/група
Mašinski fakultetTY - CONF AU - Lazarević, Mihailo PY - 2011 UR - https://machinery.mas.bg.ac.rs/handle/123456789/4763 AB - In this paper, some basic results of the stability criteria of fractional order system with time delay as well as free delay are presented. Also, they are obtained and presented sufficient conditions for finite time stability for (non)linear (non)homogeneous as well as perturbed fractional order time delay systems. Several stability criteria for this class of fractional order systems are proposed using a recently suggested generalized Gronwall inequality as well as “classical” Bellman-Gronwall inequality. Some conclusions for stability are similar to that of classical integer-order differential equations. Last, a numerical example is given to illustrate the validity of the proposed procedure. PB - Belgrade: Serbian Society of Mechanics C3 - Proceedings of the 3rd International Congress of Serbian Society of Mechanics (IConSSM 2011),Vlasina lake (Serbia), 5-8 July 2011 T1 - Stability of fractional order time delay systems EP - 69 SP - 44 UR - https://hdl.handle.net/21.15107/rcub_machinery_4763 ER -
@conference{ author = "Lazarević, Mihailo", year = "2011", abstract = "In this paper, some basic results of the stability criteria of fractional order system with time delay as well as free delay are presented. Also, they are obtained and presented sufficient conditions for finite time stability for (non)linear (non)homogeneous as well as perturbed fractional order time delay systems. Several stability criteria for this class of fractional order systems are proposed using a recently suggested generalized Gronwall inequality as well as “classical” Bellman-Gronwall inequality. Some conclusions for stability are similar to that of classical integer-order differential equations. Last, a numerical example is given to illustrate the validity of the proposed procedure.", publisher = "Belgrade: Serbian Society of Mechanics", journal = "Proceedings of the 3rd International Congress of Serbian Society of Mechanics (IConSSM 2011),Vlasina lake (Serbia), 5-8 July 2011", title = "Stability of fractional order time delay systems", pages = "69-44", url = "https://hdl.handle.net/21.15107/rcub_machinery_4763" }
Lazarević, M.. (2011). Stability of fractional order time delay systems. in Proceedings of the 3rd International Congress of Serbian Society of Mechanics (IConSSM 2011),Vlasina lake (Serbia), 5-8 July 2011 Belgrade: Serbian Society of Mechanics., 44-69. https://hdl.handle.net/21.15107/rcub_machinery_4763
Lazarević M. Stability of fractional order time delay systems. in Proceedings of the 3rd International Congress of Serbian Society of Mechanics (IConSSM 2011),Vlasina lake (Serbia), 5-8 July 2011. 2011;:44-69. https://hdl.handle.net/21.15107/rcub_machinery_4763 .
Lazarević, Mihailo, "Stability of fractional order time delay systems" in Proceedings of the 3rd International Congress of Serbian Society of Mechanics (IConSSM 2011),Vlasina lake (Serbia), 5-8 July 2011 (2011):44-69, https://hdl.handle.net/21.15107/rcub_machinery_4763 .