In this paper, we mainly study the Lyapunov asymptotical stability of linear and interval linear fractional order neutral systems with time delay. By applying the characteristic equations of these two systems, some simple sufficient Lyapunov asymptotical stability conditions are deserved, which are quite different from other ones in literature. In addition, some numerical examples are provided to demonstrate the effectiveness of our results.
Published in | Science Journal of Circuits, Systems and Signal Processing (Volume 6, Issue 1) |
DOI | 10.11648/j.cssp.20170601.11 |
Page(s) | 1-5 |
Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
Copyright |
Copyright © The Author(s), 2017. Published by Science Publishing Group |
Interval Fractional-Order Neutral Systems, Time Delay, Characteristic Equation
[1] | I. Podlubuy, Fractional differential equations. New York: Academic Press, 1999. |
[2] | Ita, J. J. and L. Stixrude, “Petrology, elasticity and composition of the transition zone,” Journal of Geophysical Research, vol. 97, pp. 6849-6866, 1992. |
[3] | A. Oustaloup, X. Morean, M. Nouiuant, “The CRONE Suspension. Control Eng. Pract.,” vol. 4 (8), pp.1101-1108. 1996. |
[4] | O. Side, Electromagnetic theory, Chelsea, New York, 1971. |
[5] | D. Matignon, “Stability Results on fractional Differential Equations to Control Processing, in: Peocessings of Computational Engineering in Syatems and Application Multiconference,” vol. 2, IMACS, IEEE-SMC, pp. 963-968, 1996. |
[6] | Y. Q. Chen, K. L. Moore, “Analytical Stability Bound for a Class of Delayed Fractional-Order Dynamic Systems,” Nonlinear Dynamics, vol. 29, pp. 191-202, 2002. |
[7] | C. Hwang, C. C. Yi, “Use of Lambert W function to Stability Analysis of Time-Delay System,” Portland, OR, USA, pp. 4283-4288. June 8-10, 2005. |
[8] | K. W. Liu, W. Jiang, “Stability of Fractional Neutral Systems,” Advanced in Differential Equations, vol. 78, pp. 1-9, 2014. |
[9] | J. Chen, D. Xu, B. Shafai, “On Sufficient Conditions for Stability Indenpendent of Delay,” IEEE Trans. Automat Control, vol. 40 (9), pp.1675-1680, 1995. |
[10] | T. Mori, “Criteria for Asymptotic Stability of Linear Time Delay Systems,” IEEE Trans. Automat Control, vol. 30 (2), pp. 158-161, 1985. |
[11] | M. Lazarevic, “Stability and Stabilization of Fractional Order Time Delay Systems,” Scientific Technical Review, vol. 61-1, pp. 31-45, 2011. |
[12] | J. Sabatier, M. Moze, C. Farges, “LMI stability conditions for fractional order systems,” Computers and Mathematics with Applications, vol. 59, pp. 1594-1609, 2010. |
[13] | M. P. Lazarevic, “Finite time stability analysis of fractional control of robotic time-delay systems: Gronwall's approach,” Mathematical and Computer Modelling, vol. 49, pp. 475-481, 2009. |
[14] | Qing-long Han, “Stability of linear neutral system with linear fractional norm-bounded uncertainty,” American Control Conference, vol. 4, pp. 2827-2832, 2005. |
[15] | C. A. Desoer, M. Vidyasagar, Feedback system: input-output properties, Academic press, New York, 1975. |
[16] | H. Li, S. M. Zhong, H. B. Li, “Stability analysis of Fractional-order systems with time delay,” International J. Mathematical, Computational Science and Engineering, vol. 8 (4), pp. 14-17, 2014. |
APA Style
Hong Li, Shou-ming Zhong, Hou-biao Li. (2017). Stability Analysis of Linear Fractional-Order Neutral Systems with Time Delay. Science Journal of Circuits, Systems and Signal Processing, 6(1), 1-5. https://doi.org/10.11648/j.cssp.20170601.11
ACS Style
Hong Li; Shou-ming Zhong; Hou-biao Li. Stability Analysis of Linear Fractional-Order Neutral Systems with Time Delay. Sci. J. Circuits Syst. Signal Process. 2017, 6(1), 1-5. doi: 10.11648/j.cssp.20170601.11
AMA Style
Hong Li, Shou-ming Zhong, Hou-biao Li. Stability Analysis of Linear Fractional-Order Neutral Systems with Time Delay. Sci J Circuits Syst Signal Process. 2017;6(1):1-5. doi: 10.11648/j.cssp.20170601.11
@article{10.11648/j.cssp.20170601.11, author = {Hong Li and Shou-ming Zhong and Hou-biao Li}, title = {Stability Analysis of Linear Fractional-Order Neutral Systems with Time Delay}, journal = {Science Journal of Circuits, Systems and Signal Processing}, volume = {6}, number = {1}, pages = {1-5}, doi = {10.11648/j.cssp.20170601.11}, url = {https://doi.org/10.11648/j.cssp.20170601.11}, eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.cssp.20170601.11}, abstract = {In this paper, we mainly study the Lyapunov asymptotical stability of linear and interval linear fractional order neutral systems with time delay. By applying the characteristic equations of these two systems, some simple sufficient Lyapunov asymptotical stability conditions are deserved, which are quite different from other ones in literature. In addition, some numerical examples are provided to demonstrate the effectiveness of our results.}, year = {2017} }
TY - JOUR T1 - Stability Analysis of Linear Fractional-Order Neutral Systems with Time Delay AU - Hong Li AU - Shou-ming Zhong AU - Hou-biao Li Y1 - 2017/03/04 PY - 2017 N1 - https://doi.org/10.11648/j.cssp.20170601.11 DO - 10.11648/j.cssp.20170601.11 T2 - Science Journal of Circuits, Systems and Signal Processing JF - Science Journal of Circuits, Systems and Signal Processing JO - Science Journal of Circuits, Systems and Signal Processing SP - 1 EP - 5 PB - Science Publishing Group SN - 2326-9073 UR - https://doi.org/10.11648/j.cssp.20170601.11 AB - In this paper, we mainly study the Lyapunov asymptotical stability of linear and interval linear fractional order neutral systems with time delay. By applying the characteristic equations of these two systems, some simple sufficient Lyapunov asymptotical stability conditions are deserved, which are quite different from other ones in literature. In addition, some numerical examples are provided to demonstrate the effectiveness of our results. VL - 6 IS - 1 ER -