On the Stability Analysis of Systems of Neutral Delay Differential Equations
- 44 Downloads
This paper focuses on the stability analysis of systems modeled as neutral delay differential equations (NDDEs). These systems include delays in both the state variables and their time derivatives. The proposed approach consists of a descriptor model transformation that constructs an equivalent set of delay differential algebraic equations (DDAEs) of the original NDDEs. We first rigorously prove the equivalency between the original set of NDDEs and the transformed set of DDAEs. Then, the effect on stability analysis is evaluated numerically through a delay-independent stability criterion and the Chebyshev discretization of the characteristic equations.
KeywordsTime delay Delay differential algebraic equations (DDAEs) Neutral time-delay differential equations (NDDEs) Eigenvalue analysis Delay-independent stable
This material is supported by the Science Foundation Ireland, by funding Muyang Liu, Ioannis Dassios and Federico Milano, under Investigator Programme Grant No. SFI/15/IA/3074.
- 16.V.B. Kolmanovskii, V.R. Nosov, Stability and Periodic Modes of Control Systems with Aftereffect (Moscow, Russia, 1981)Google Scholar
- 17.P. Kundur, N. Balu, Power System Stability and Control. EPRI Power System Engineering Series (McGraw-Hill, New York, 1994)Google Scholar
- 19.D. Liu, Q. Zheng, Stability Analysis of Neutral Systems with Distributed Delays in 7th International Conference on Advanced Intelligent Computing (Zhengzhou, China, 2011)Google Scholar
- 20.M. Liu, I. Dassios, F. Milano, Small-Signal Stability Analysis of Neutral Delay Differential Equation in 43th Annual Conference of the IEEE Industrial Electronics Society (IECON 2017) (Beijing, China, 2017)Google Scholar
- 23.F. Milano, A Python-Based Software Tool for Power System Analysis, in Proceedings of the IEEE PES General Meeting (Vancouver, BC, 2013)Google Scholar
- 27.B.M. Pao, C. Liu, G. Yin, Topics in Stochastic Analysis and Nonparametric Estimation (Science Business Media, New York, 2008)Google Scholar