Kybernetika 57 no. 5, 776-784, 2021

New criteria for exponential stability of linear neutral differential systems with distributed delays

Pham Huu Anh Ngoc, Thai Bao Tran and Nguyen Dinh HuyDOI: 10.14736/kyb-2021-5-0776

Abstract:

We present new explicit criteria for exponential stability of general linear neutral time-varying differential systems. Particularly, our results give extensions of the well-known stability criteria reported in \cite{Bel99,Li88} to linear neutral time-varying differential systems with distributed delays.

Keywords:

exponential stability, time-varying systems, linear neutral differential equation

Classification:

34K20

References:

  1. R. P. Agarwal and S. R. Grace: Asymptotic stability of certain neutral differential equations. Math.Computer Modell. 31 (2000), 9-15.   DOI:10.7748/ns.15.9.31.s55
  2. I. V. Alexandrova and A. P. Zhabko: Stability of neutral type delay systems: A joint Lyapunov-Krasovskii and Razumikhin approach. Automatica 106 (2019), 83-90.   DOI:10.1016/j.automatica.2019.04.036
  3. A. Bellen, N. Guglielmi and A. E. Ruehli: Methods for linear systems of circuit delay differential equations of neutral type. IEEE Trans. Circuits Systems I Fundamental Theory Appl. 46 (1999), 212-215.   DOI:10.1109/81.739268
  4. J Duda: A Lyapunov functional for a neutral system with a time-varying delay. Bull. Polish Acad. Sci.: Techn. Sci. 61 (2013), 911-918.   CrossRef
  5. CA. Desoer and M. Vidyasagar: Feedback Synthesis: Input-Output Properties. SIAM, Philadelphia 2009.   CrossRef
  6. E. Fridman: New Lyapunov-Krasovskii functionals for stability of linear retarded and neutral type systems. Systems Control Lett. 43 (2001), 309-319.   DOI:10.1524/itit.2001.43.6.309
  7. M. Gil: Stability of Neutral Functional Differential Equations. Atlantis Press, Amsterdam, Paris, Bejing 2014.   CrossRef
  8. J. Hale and S. Lunel: Introduction to Functional Differential Equations. Springer-Verlag, Berlin 1993.   CrossRef
  9. G. D. Hu and G. D. Hu: Simple criteria for stability of neutral systems with multiple delays. Int. J. Systems Science 28 (1997), 1325-1328.   DOI:10.1524/itit.2001.43.6.309
  10. V. Kolmanovskii and A. Mishkis: Introduction to the Theory and Applications of Functional Differential Equations: Mathematics and its Applications. Kluwer Academic Publisher, Dordreht 1999.   CrossRef
  11. L. Li: Stability of linear neutral delay-differential systems. Bull. Austral. Math. Soc. 38 (1988), 339-344.   DOI:10.1017/S0004972700027684
  12. Z. Li, J. Lam and Y. Wang: Stability analysis of linear stochastic neutral-type time-delay systems with two delays. Automatica 91 (2018), 179-189.   DOI:10.1016/j.automatica.2018.01.014
  13. P. H. A. Ngoc and H. Trinh: Novel criteria for exponential stability of linear neutral time-varying differential systems. IEEE Trans. Automat. Control 61 (2016), 1590-1594.   DOI:10.1109/TAC.2015.2478125
  14. E. Verriest and S. Niculescu: Delay-independent stability of linear neutral systems: A Riccati equation approach. In: Stability and Control of Time-Delay Systems (L. Dugard and E. I. Verriest, eds.), Springer-Verlag, London 1998, pp. 92-100.   CrossRef
  15. N. Zhao, X. Zhang, Y. Xue and P. Shi: Necessary conditions for exponential stability of linear neutral type systems with multiple time delays. J. Franklin Inst. 355 (2018), 458-473.   DOI:10.1016/j.jfranklin.2017.11.016