American Institute of Mathematical Sciences

Advanced
January  2007, 17(1): 95-105. doi: 10.3934/dcds.2007.17.95

Characteristic equation approach to stability measures of linear neutral systems with multiple time delays

D. Q. Cao 1, , Y. R. Yang 2, and  Y. M. Ge 2,

1. 

Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom
2. 

Department of Applied Mechanics and Engineering, Southwest Jiaotong University, Chengdu 610031, China, China

Received  February 2006 Revised  July 2006 Published  October 2006

Using the characteristic equation approach, the problem of asymptotic stability of linear neutral systems with multiple time delays is investigated in this paper. New delay-independent stability criteria are derived in terms of the spectral radius of corresponding modulus matrices. The structure information of the system matrices are taken into consideration in the proposed stability criteria, thus the conservatism found in the literature can be significantly reduced. The explicit nature of the construction permits us to directly express the algebraic criteria in terms of the plant parameters, thus checking of stability by our criteria can be carried out rather simply. Numerical examples are given to demonstrate the validity of the new criteria and to compare them with the previous results.
Keywords: Neutral systems, stability, algebraic criteria, multiple time delays..
Mathematics Subject Classification: Primary: 34K06, 39B82; Secondary: 37C7.
Citation: D. Q. Cao, Y. R. Yang, Y. M. Ge. Characteristic equation approach to stability measures of linear neutral systems with multiple time delays. Discrete & Continuous Dynamical Systems - A, 2007, 17 (1) : 95-105. doi: 10.3934/dcds.2007.17.95
[1]

Jan Čermák, Jana Hrabalová. Delay-dependent stability criteria for neutral delay differential and difference equations. Discrete & Continuous Dynamical Systems - A, 2014, 34 (11) : 4577-4588. doi: 10.3934/dcds.2014.34.4577
[2]

Zhaohua Gong, Chongyang Liu, Yujing Wang. Optimal control of switched systems with multiple time-delays and a cost on changing control. Journal of Industrial & Management Optimization, 2018, 14 (1) : 183-198. doi: 10.3934/jimo.2017042
[3]

Hongbiao Fan, Jun-E Feng, Min Meng. Piecewise observers of rectangular discrete fuzzy descriptor systems with multiple time-varying delays. Journal of Industrial & Management Optimization, 2016, 12 (4) : 1535-1556. doi: 10.3934/jimo.2016.12.1535
[4]

Wei Wang, Kai Liu, Xiulian Wang. Sensitivity to Small Delays of Mean Square Stability for Stochastic Neutral Evolution Equations. Communications on Pure & Applied Analysis, 2020, 19 (4) : 2403-2418. doi: 10.3934/cpaa.2020105
[5]

Ábel Garab, Veronika Kovács, Tibor Krisztin. Global stability of a price model with multiple delays. Discrete & Continuous Dynamical Systems - A, 2016, 36 (12) : 6855-6871. doi: 10.3934/dcds.2016098
[6]

Masakatsu Suzuki, Hideaki Matsunaga. Stability criteria for a class of linear differential equations with off-diagonal delays. Discrete & Continuous Dynamical Systems - A, 2009, 24 (4) : 1381-1391. doi: 10.3934/dcds.2009.24.1381
[7]

Wei Feng, Xin Lu. Global stability in a class of reaction-diffusion systems with time-varying delays. Conference Publications, 1998, 1998 (Special) : 253-261. doi: 10.3934/proc.1998.1998.253
[8]

Desheng Li, P.E. Kloeden. Robustness of asymptotic stability to small time delays. Discrete & Continuous Dynamical Systems - A, 2005, 13 (4) : 1007-1034. doi: 10.3934/dcds.2005.13.1007
[9]

Zhen Jin, Zhien Ma. The stability of an SIR epidemic model with time delays. Mathematical Biosciences & Engineering, 2006, 3 (1) : 101-109. doi: 10.3934/mbe.2006.3.101
[10]

Laurenz Göllmann, Helmut Maurer. Theory and applications of optimal control problems with multiple time-delays. Journal of Industrial & Management Optimization, 2014, 10 (2) : 413-441. doi: 10.3934/jimo.2014.10.413
[11]

Cheng-Hsiung Hsu, Suh-Yuh Yang. Traveling wave solutions in cellular neural networks with multiple time delays. Conference Publications, 2005, 2005 (Special) : 410-419. doi: 10.3934/proc.2005.2005.410
[12]

M.I. Gil’. Existence and stability of periodic solutions of semilinear neutral type systems. Discrete & Continuous Dynamical Systems - A, 2001, 7 (4) : 809-820. doi: 10.3934/dcds.2001.7.809
[13]

Mark A. Pinsky, Alexandr A. Zevin. Stability criteria for linear Hamiltonian systems with uncertain bounded periodic coefficients. Discrete & Continuous Dynamical Systems - A, 2005, 12 (2) : 243-250. doi: 10.3934/dcds.2005.12.243
[14]

Serge Nicaise, Julie Valein, Emilia Fridman. Stability of the heat and of the wave equations with boundary time-varying delays. Discrete & Continuous Dynamical Systems - S, 2009, 2 (3) : 559-581. doi: 10.3934/dcdss.2009.2.559
[15]

David Schley, S.A. Gourley. Linear and nonlinear stability in a diffusional ecotoxicological model with time delays. Discrete & Continuous Dynamical Systems - B, 2002, 2 (4) : 575-590. doi: 10.3934/dcdsb.2002.2.575
[16]

Shengqin Xu, Chuncheng Wang, Dejun Fan. Stability and bifurcation in an age-structured model with stocking rate and time delays. Discrete & Continuous Dynamical Systems - B, 2019, 24 (6) : 2535-2549. doi: 10.3934/dcdsb.2018264
[17]

Ye Chen, Keith W. Hipel, D. Marc Kilgour. A multiple criteria sequential sorting procedure. Journal of Industrial & Management Optimization, 2008, 4 (3) : 407-423. doi: 10.3934/jimo.2008.4.407
[18]

Zhigang Zeng, Tingwen Huang. New passivity analysis of continuous-time recurrent neural networks with multiple discrete delays. Journal of Industrial & Management Optimization, 2011, 7 (2) : 283-289. doi: 10.3934/jimo.2011.7.283
[19]

Tingwen Huang, Guanrong Chen, Juergen Kurths. Synchronization of chaotic systems with time-varying coupling delays. Discrete & Continuous Dynamical Systems - B, 2011, 16 (4) : 1071-1082. doi: 10.3934/dcdsb.2011.16.1071
[20]

Wei Feng, Xin Lu. Global periodicity in a class of reaction-diffusion systems with time delays. Discrete & Continuous Dynamical Systems - B, 2003, 3 (1) : 69-78. doi: 10.3934/dcdsb.2003.3.69

2018 Impact Factor: 1.143

Tools

Metrics

  • PDF downloads (20)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences