Finite-Time Stability of Fractional Time Delay System
Abstract
In this study, some basic results of the stability criteria of fractional order systems with time-delay as well as free-delay are presented. Particularly, 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 those of classical integer-order differential equations. Lastly, numerical examples are given to illustrate the validity of the proposed procedure.
Keywords:
stability / fractional calculus / time-delay / fractional order system / finite-time stabilitySource:
Advanced Topics on Applications of Fractional Calculus on Control Problems, System Stability and Modeling, 2014, 43-66Publisher:
- WSEAS Press
Funding / projects:
- Sustainability and improvement of mechanical systems in energetic, material handling and conveying by using forensic engineering, environmental and robust design (RS-MESTD-Technological Development (TD or TR)-35006)
- Development of methods and techniques for early diagnostic of cervical, colon, oral cavity cancer and melanoma based on a digital image and excitation-emission spectrum in visible and infrared domain (RS-MESTD-Integrated and Interdisciplinary Research (IIR or III)-41006)
- Energy efficiency Improvement of Hydro and Thermal power plants in EPS by development and implementation of power electronics based regulation and automation equipment (RS-MESTD-Technological Development (TD or TR)-33020)
- Dynamics of hybrid systems with complex structures. Mechanics of materials. (RS-MESTD-Basic Research (BR or ON)-174001)
Collections
Institution/Community
Mašinski fakultetTY - CHAP AU - Lazarević, Mihailo PY - 2014 UR - https://machinery.mas.bg.ac.rs/handle/123456789/6684 AB - In this study, some basic results of the stability criteria of fractional order systems with time-delay as well as free-delay are presented. Particularly, 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 those of classical integer-order differential equations. Lastly, numerical examples are given to illustrate the validity of the proposed procedure. PB - WSEAS Press T2 - Advanced Topics on Applications of Fractional Calculus on Control Problems, System Stability and Modeling T1 - Finite-Time Stability of Fractional Time Delay System EP - 66 SP - 43 UR - https://hdl.handle.net/21.15107/rcub_machinery_6684 ER -
@inbook{ author = "Lazarević, Mihailo", year = "2014", abstract = "In this study, some basic results of the stability criteria of fractional order systems with time-delay as well as free-delay are presented. Particularly, 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 those of classical integer-order differential equations. Lastly, numerical examples are given to illustrate the validity of the proposed procedure.", publisher = "WSEAS Press", journal = "Advanced Topics on Applications of Fractional Calculus on Control Problems, System Stability and Modeling", booktitle = "Finite-Time Stability of Fractional Time Delay System", pages = "66-43", url = "https://hdl.handle.net/21.15107/rcub_machinery_6684" }
Lazarević, M.. (2014). Finite-Time Stability of Fractional Time Delay System. in Advanced Topics on Applications of Fractional Calculus on Control Problems, System Stability and Modeling WSEAS Press., 43-66. https://hdl.handle.net/21.15107/rcub_machinery_6684
Lazarević M. Finite-Time Stability of Fractional Time Delay System. in Advanced Topics on Applications of Fractional Calculus on Control Problems, System Stability and Modeling. 2014;:43-66. https://hdl.handle.net/21.15107/rcub_machinery_6684 .
Lazarević, Mihailo, "Finite-Time Stability of Fractional Time Delay System" in Advanced Topics on Applications of Fractional Calculus on Control Problems, System Stability and Modeling (2014):43-66, https://hdl.handle.net/21.15107/rcub_machinery_6684 .