Stability of Discrete-Time Fractional Order Systems considered: An Approach Based on Stability of Discrete-Time Integer Order Time-Delay Systems
Abstract
In this paper the problem of stability of linear discrete-time fractional order systems is addressed. It
was shown that some stability criteria for discrete time-delay systems could be applied with small changes to discrete fractional order state-space systems. Accordingly, simple conditions for the stability and robust stability of a particular class of linear discrete time-delay systems are derived. These results are modified and used for checking the stability of discrete-time fractional order systems. The systems under consideration involve time delays in the state and parameter uncertainties. The parameter uncertainties are assumed to be time-varying and norm bounded. New Lyapunov–Krasovskii functional is constructed to derive some delay dependent stability criteria. The proposed methods give both sufficient and necessary and sufficient stability
conditions. Numerical examples have been worked out to show the applicability of the derived results.
Keywords:
Discrete-time fractional order systems / discrete time-delay systems / stability / robust stability / Lyapunov functional / delay-independent stability / delay-dependent stabilitySource:
Advanced Topics on Applications of Fractional Calculus on Control Problems, System Stability and Modeling, 2014, 67-87Publisher:
- 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 - Stojanović, Sreten AU - Debeljković, Dragutin AU - Lazarević, Mihailo PY - 2014 UR - https://machinery.mas.bg.ac.rs/handle/123456789/6685 AB - In this paper the problem of stability of linear discrete-time fractional order systems is addressed. It was shown that some stability criteria for discrete time-delay systems could be applied with small changes to discrete fractional order state-space systems. Accordingly, simple conditions for the stability and robust stability of a particular class of linear discrete time-delay systems are derived. These results are modified and used for checking the stability of discrete-time fractional order systems. The systems under consideration involve time delays in the state and parameter uncertainties. The parameter uncertainties are assumed to be time-varying and norm bounded. New Lyapunov–Krasovskii functional is constructed to derive some delay dependent stability criteria. The proposed methods give both sufficient and necessary and sufficient stability conditions. Numerical examples have been worked out to show the applicability of the derived results. PB - WSEAS Press T2 - Advanced Topics on Applications of Fractional Calculus on Control Problems, System Stability and Modeling T1 - Stability of Discrete-Time Fractional Order Systems considered: An Approach Based on Stability of Discrete-Time Integer Order Time-Delay Systems EP - 87 SP - 67 UR - https://hdl.handle.net/21.15107/rcub_machinery_6685 ER -
@inbook{ author = "Stojanović, Sreten and Debeljković, Dragutin and Lazarević, Mihailo", year = "2014", abstract = "In this paper the problem of stability of linear discrete-time fractional order systems is addressed. It was shown that some stability criteria for discrete time-delay systems could be applied with small changes to discrete fractional order state-space systems. Accordingly, simple conditions for the stability and robust stability of a particular class of linear discrete time-delay systems are derived. These results are modified and used for checking the stability of discrete-time fractional order systems. The systems under consideration involve time delays in the state and parameter uncertainties. The parameter uncertainties are assumed to be time-varying and norm bounded. New Lyapunov–Krasovskii functional is constructed to derive some delay dependent stability criteria. The proposed methods give both sufficient and necessary and sufficient stability conditions. Numerical examples have been worked out to show the applicability of the derived results.", publisher = "WSEAS Press", journal = "Advanced Topics on Applications of Fractional Calculus on Control Problems, System Stability and Modeling", booktitle = "Stability of Discrete-Time Fractional Order Systems considered: An Approach Based on Stability of Discrete-Time Integer Order Time-Delay Systems", pages = "87-67", url = "https://hdl.handle.net/21.15107/rcub_machinery_6685" }
Stojanović, S., Debeljković, D.,& Lazarević, M.. (2014). Stability of Discrete-Time Fractional Order Systems considered: An Approach Based on Stability of Discrete-Time Integer Order Time-Delay Systems. in Advanced Topics on Applications of Fractional Calculus on Control Problems, System Stability and Modeling WSEAS Press., 67-87. https://hdl.handle.net/21.15107/rcub_machinery_6685
Stojanović S, Debeljković D, Lazarević M. Stability of Discrete-Time Fractional Order Systems considered: An Approach Based on Stability of Discrete-Time Integer Order Time-Delay Systems. in Advanced Topics on Applications of Fractional Calculus on Control Problems, System Stability and Modeling. 2014;:67-87. https://hdl.handle.net/21.15107/rcub_machinery_6685 .
Stojanović, Sreten, Debeljković, Dragutin, Lazarević, Mihailo, "Stability of Discrete-Time Fractional Order Systems considered: An Approach Based on Stability of Discrete-Time Integer Order Time-Delay Systems" in Advanced Topics on Applications of Fractional Calculus on Control Problems, System Stability and Modeling (2014):67-87, https://hdl.handle.net/21.15107/rcub_machinery_6685 .
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