Stability Analysis of Linear Fractional Order Neutral System with Multiple Delays by Algebraic Approach
In this paper, we study the stability of n-dimensional linear fractional neutral differential equation with time delays. By using the Laplace transform, we introduce a characteristic equation for the above system with multiple time delays. We discover that if all roots of the characteristic equation have negative parts, then the equilibrium of the above linear system with fractional order is Lyapunov globally asymptotical stable if the equilibrium exist that is almost the same as that of classical differential equations. An example is provided to show the effectiveness of the approach presented in this paper.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1059641Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2004
 M.-W. Spong, A theorem on neutral delay systems Original Research Article Systems & Control Letters, 6(1985): 291-294.
 Y. He, M. Wu, J.-H. She, G.-P. Liu, Delay-dependent robust stability criteria for uncertain neutral systems with mixed delays, Systems & Control Letters, 51(2004): 57-65.
 C.-H. Lien, K.-W. Yu, Y.-J. Chung, Y.-F. Lin, L.-Y. Chung, J.-D. Chen, Exponential stability analysis for uncertain switched neutral systems with interval-time-varying state delay, Nonlinear Analysis: Hybrid Systems, 3(2009):334-342.
 L.-L. Xiong, S.-M. Zhong, M. Ye, S.-L. Wu, New stability and stabilization for switched neutral control systems Original Research Article Chaos, Solitons & Fractals, 42(2009):1800-1811.
 X.-G. Liu, M. Wu, Ralph Martin, M.-L. Tang, Stability analysis for neutral systems with mixed delays Original Research Article Journal of Computational and Applied Mathematics, 202(2007):478-497.
 L.-L. Xiong, S.-M. Zhong, J.-K. Tian, Novel robust stability criteria of uncertain neutral systems with discrete and distributed delays, Chaos, Solitons & Fractals, 40(2009):771-777.
 W.-J. Xiong , J.-L. Liang. Novel stability criteria for neutral systems with multiple time delays. Chaos,solitions & Fractals, 32(2007): 1735-1741.
 H. Li, H.-B. Li, S.-M. Zhong. Some new simple stability criteria of linear neutral systems with a single delay. Journal of Computational and Applied Mathematics, 200(2007):441-447.
 W.-H. Deng, C.-P. Li, J.-H. Lv, Stability analysis of linear fractional differential system with multiple time delays, Nonlinear Dynamics, 48(2007):409-416.
 Y.-Q. Chen, H.S. Ahn, I. Podlubny, Robust stability check of fractional order linear time invariant systems with interval uncertainties. Signal Process, 86(2006):2611-2618.
 H.-S. Ahn, Y.-Q. Chen, I. Podlubny, Robust stability test of a class of linear time-invariant interval fractional-order system using Lyapunov inequality. Appl.Math Comput, 187(2007):27-34.
 Moze M, Sabatier J. LMI tools for stability analysis of fractional systems. In: Proceedings ASME 2005 international design engineering technical conferences & computers and information in engineering conference, Paper DETC2005-85182, Long Beach, CA, USA, September 24- 28, 2005.
 Petras I, Chen Y, Vinagre BM. Robust stability test for interval fractional order linear systems. In: Blondel VD, Megretski A, editors. Unsolved problems in the mathematics of systems and control, vols. 208210. Princeton, NJ: Princeton University Press; 2004
 Petras I, Chen Y, Vinagre BM, Podlubny I. Stability of linear time invariant systems with interval fractional orders and interval coefficients. In: Proceedings of the international conference on computation cybernetics (ICCC04), Vienna Technical University, Vienna, Austria, 8/30-9/1; 2005. p. 14.
 R. Hotzel, Some stability conditions for fractional delay systems. J Math Syst Estimat Control, 8(1998):1-9.
 C. Hwang, Y.C. Cheng, A numerical algorithm for stability testing of fractional delay systems, Automatica, 42 (2006): 825-831.
 D. Matignon, Stability properties for generalized fractional differential systems, ESAIM: Proc. 5 (1998): 145-158.
 P. Ostalczyk, Nyquist characteristics of a fractional order integrator, Journal of Fractional Calculus, 19(2001):67-78.
 Mohammad Saleh Tavazoei, Mohammad Haeri, Sadegh Bolouki, Milad Siami, Stability preservation analysis for frequency-based methods in numerical simulation of fractional order systems, Siam Journal of Numerical Analysis, 47(2008): 321-338.
 J.-G. Lu, Y.-Q. Chen, Robust Stability and Stabilization of Fractional- Order Interval Systems with the Fractional Order ╬▒: The 0 < ╬▒ < 1 case, IEEE transactions on automatic control, 55(2010): 152-158.
 Z.-X. Tai, X.-C. Wang, Controllability of fractional-order impulsive neutral functional infinite delay integrodifferential systems in Banach spaces, Applied Mathematics Letters, 22(2009):1760-1765.
 Y. Zhou, F. Jiao, J. Li, Existence and uniqueness for fractional neutral differential equations with infinite delay, Nonlinear Analysis: Theory, Methods & Applications, 71(2009): 3249-3256.
 Y. Zhou, F. Jiao, J. Li, Existence and uniqueness for p− type fractional neutral differential equations, Nonlinear Analysis: Theory, Methods & Applications, 71(2009):2724-2733.
 R.P. Agarwal, Y. Zhou, Y.-Y. He, Existence of fractional neutral functional differential equations,
 Y. Zhou, F. Jiao, Computers and Mathematics with Applications, 59(2010):1095-1100.
 Y. Zhou, F. Jiao, Existence of mild solutions for fractional neutral evolution equations, Computers and Mathematics with Applications, 59(2010):1063-1077.
 G.M. Mophou, G. M. N-Guerekata, Existence of mild solutions of some semilinear neutral fractional functional evolution equations with infinite delay, Applied Mathematics and Computation, 216(2010):61-69.
 Kamran Akbari Moornani, Mohammad Haeri, On robust stability of LTI fractional-order delay systems of retarded and neutral type, Automatica 46 (2010) 362-368.
 A.-H. Lin, Y. Ren, N.-M. Xia, On neutral impulsive stochastic integrodifferential equations with infinite delays via fractional operators, Mathematical and Computer Modelling, 51(2010):413-424.
 G.-D. Hu, Some new simple stability criteria of neutral delay-differential systems, Applied mathematics and computaiton, 80(1996):257-271.
 D.-Q. Cao, P. He, Stability criteria of linear neutral systems with a single delay, Applied Mathematics and Computation, 148(2004):135-143.
 E.J. Muth, Transform Methods with Applications to Engineering and Operations Research. Prentice-Hall, New Jersey, 1977.
 P. Lancaster, M. Tismenetsky, The Theory of Matrices, Academic Press, Orlando, FL, 1985.