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Robust Delay Dependent Stability Analysis of Neutral Systems

  • Salvador A. Rodriguez
  • Jean-Michel Dion
  • Luc Dugard
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 38)

Abstract

This chapter focuses on the delay-dependent robust stability of linear neutral delay systems. The systems under consideration are described by functional differential equations, with norm bounded time varying nonlinear uncertainties in the “state”, in the delayed “state” and norm bounded time varing quasilinear uncertainties in the difference operator. Two unknown constant delays, in the delayed “stale” and in the difference operator, lead to consider a more general delay-dependent robust stability problem. The analysis is performed via Lyapunov-Krasovskii functional approach. The main difference with respect to 18 is that we obtain sufficient conditions for robust stability given in tenns of the existence of positive dcfinite solutions of LMIs. Thc proposed stability analysis extends some previous results on the subject.

Keywords

Robust Stability Functional Differential Equation Time Delay System Neutral System Neutral Functional Differential Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Bellen A., N. Guglielmi and A.E. Ruehli (1999) Methods for Linear Systems of Circuits Delays Differential Equations of Neutral Type. IEEE Trans. Circuits and Sys. 461:212–216.MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Boyd S., L.EI Ghaoui, E. Feron and V. Balakrishnan (1994) Linear Matrix Inequalities in System and Control Theory. Society for Industrial and Applied Mathematics.Google Scholar
  3. 3.
    Brayton R. (1976) Nonlinear Oscillations in a Distributed Network, Quart. Appl. Math., 24: 289–301.MathSciNetGoogle Scholar
  4. 4.
    Bums J. A. Herdman T.L and Stech H.W (1983) Linear Functional Differential Equations As Semigroups On Products Spaces. SIAM. J. Math. Anal., 14:98–116.Google Scholar
  5. 5.
    Chen J. (1995) On Computing the Maximal Delay Intervals for Stability of Linear Delay Systems. IEEE Trans. Automat. Contr., 40: 1087–1093.zbMATHCrossRefGoogle Scholar
  6. 6.
    Cruz M.A. and J.K. Hale (1970) Stability of functional differential equations of neutral type. J. Differential Eqns. 7:334–355.MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Diekmann O., S.A. van Gils, S.M. Verduyn Lunel and H.-O. Waither (1995). Delay Equations Functional-, Complex-, and Nonlinear Analysis. Springer Verlag.Google Scholar
  8. 8.
    Hale J.K. and M.A. Cruz (1970) Existence, Uniqueness and Continuous Dependence for Hereditary Systems. Ann. Mat. Pura Appl. 854:63–82.MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Hale J.K. and S.M. Verduyn Lunel (1993) Introduction to Functional Differential Equations. Springer-Verlag.Google Scholar
  10. 10.
    Henry D. (1974) Linear Autonomous Neutral Functional Differential Equations. J. Diff. Equ., 15:106–128.MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Ivanescu D., S. Niculescu, L. Dugard, J.M. Dion and E.I. Verriest (2003) On Dclay Dependent Stability for Li near Neutral Systems. Automatica. 39:255–261.MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Kharitonov V.L. (1998) Robust Stability Analysis of lime-Delay Systems; a survey. Proc. IFAC Syst. Struct. &amp Contr., Nantes, France:1–12.Google Scholar
  13. 13.
    Kolmanovskii V.B. (1996) The stability of Hereditary Systems of neutral type. J. Appl. Maths. Mechs. 60, 2:205–216.MathSciNetCrossRefGoogle Scholar
  14. 14.
    Kolmanovskii V.B. and A.D. Myshkis (1999) Introduction to the Theory and Applications of Functional Differential Equations. Kluwer Academic Publishers.Google Scholar
  15. 15.
    Kolmanovskii V.B. and J.P. Richard (1998) Stability of systems with pure, discrete multi-delays. IFAC Conference System Structure and Control Nantes, France: 13–18.Google Scholar
  16. 16.
    Niculescu S.I. (2001) On Robust Stability of Neutral Systems, Special issue On Time-Delay Systems. Kybemetica 37:253–263.MathSciNetzbMATHGoogle Scholar
  17. 17.
    Rodriguez S.A., J.M. Dion, L. Dugard and D. Ivănescu (2001) On delay-dependcnt robust stability of neutral systems. 3rd IFAC Workshop on Time Delay Systems, Santa Fe USA: 101–106.Google Scholar
  18. 18.
    Rodriguez S.A., J.M. Dion and L. Dugard. (2002) Robust Stability Analysis of Neutral Systems Under Model Transformation. 41st IEEE Conference on Decision and Control, Las Vegas, Nevada, USA: 1850–1855.Google Scholar
  19. 19.
    Verriest E.I. and S.I. Niculescu (1997) Delay-Independent Stability of LNS: A Riccati Equation Approach, in Stability and Control of Time-Delay Systems. (L. Dugard and E.I. Verriest, Eds.), Springer-Verlag L 228:92–100.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Salvador A. Rodriguez
    • 1
  • Jean-Michel Dion
    • 1
  • Luc Dugard
    • 1
  1. 1.Laboratoire d’Automatique de Grenoble (INPG CNRS UJF) ENSIEGSt. Martin d’HèresFrance

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