Control of Systems with Input Delay—An Elementary Approach

  • Vladimir Răsvan
  • Dan Popescu
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 38)


The stabilization by feedback control of systems with input delays may be considered in various frameworks; a very popular is the abstract one, based on the inclusion of such systems in the Pritchard-Salamon class. In this chapter we consider the elementary approach based on variants of the Smith predictor, make a system theoretic analysis of the compensator and suggest a computer control implementation. This implementation is based on piecewise constant control which associates a discrete-time finite dimensional control system; it is this system which is stabilized, thus avoiding unpleasant phenomena induced by the essential spectrum of other implementations


Functional Differential Equation Admissible Pair Feedback Stabilization Input Delay Smith Predictor 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Anstein Z ([1982) Lincar Systcms with Delayed Controls: a Reduction. IEEE Trans Aut Control 27:869–879CrossRefGoogle Scholar
  2. 2.
    Drăgan V, Halanay A (1999) Stabilization of Linear Systems. Birkhauscr Verlag BostonzbMATHCrossRefGoogle Scholar
  3. 3.
    Fiagbedzi Y A, Pearson A E (1986) Feedback Stabilization of autonomous Time-lag Systems. IEEE Trans Aut Control 31:847–855MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Fiagbedzi Y A, Pearson A E (1987) A Multistage Reduction Technique for Feedback Stabilizing Distributed Time-lag Systems. Automatica 23:311–326MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Halanay A, Răsvan VI (1977) General Theory of Linear Hybrid Control. Int J Control 20;621–634CrossRefGoogle Scholar
  6. 6.
    Hale J K, Verduyn Lunel S M (1993) Introduction to Functional Differential Equations. Springer Berlin Heidelberg New YorkzbMATHGoogle Scholar
  7. 7.
    Ichikawa A (1982) Quadratic control of evolution equations with delays in control. SIAM J. Control 27:12–22MathSciNetGoogle Scholar
  8. 8.
    Kwon W H, Pearson A E (1980) Feedback stabilization of linear systems with delayed control. IEEE Trans Aut Control 25:266–269MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Manitius A, Olbrot A W (1979) Finite spectrum assignment for systems with delays. IEEE Trans Aut Control 24:541–553MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Mirkin L, Tadmor G (2002) H∞ control of systems with I/O delay: a review of some problem-oriented methods. IMA Journ Math Contr Inf 19: 185–199MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Olbrot A W (1978) Stabilizability, detectability and spectrum assignment for linear systems with general time delays. IEEE Trans Aut Control 23:887–890MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Pandolfi L (1981) A state space approach 10 control systems with delayed controls. In: Kisielewicz M (ed) Proceedings of Conference on Functional Differential Equations and Related Topies Zielona Gora, PolandGoogle Scholar
  13. 13.
    Pandolfi L (1989) Dynamic stabilization of systems with input delays. In: System Structure and Control: State Space and Polynomial Methods. PragueGoogle Scholar
  14. 14.
    Pandolfi L (1990) Generalized control systems, boundary control systems and delayed control systems. Math Contr Sign Syst 3: 165–181MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    Pandolfi L (1991) Dynamic stabilization of systems wilh input delays. AutOmatica 27:1047–1050MathSciNetCrossRefGoogle Scholar
  16. 16.
    Pearson A E (2003) Parallel Systcm Modeling for Observer based Control of Input Delayed Plants. 4th Int Conference on Dynamic Syst Appl, Atlanta, 21–24 May, 2003Google Scholar
  17. 17.
    Popov V M (1960) Stability criteria for systems containing non-univocal clements (in Romanian). In: Probleme de Automatizare III:143–151, Ed.Academiei BucharestGoogle Scholar
  18. 18.
    Răsvan VI (1998) Dynamical systems with lossless propagation and neutml functional differential equations. In: Mathem Theory of Networks and Systems MTNS98. Il Poligrafo PadovaGoogle Scholar
  19. 19.
    Răsvan VI, Popescu D (2001) Feedback Stabilization of Systems with Delays in Control. Control Engineering and Applied Informatics 3:62–66Google Scholar
  20. 20.
    Răsvan VI, Popescu D (2001) Control of systems with input delay by piecewise constant signals. 9th Medit. Conf. on Control and Automation, Paper WM1-B/122, Dubrovnik, CroatiaGoogle Scholar
  21. 21.
    Tadmor G (1995) The Nehari problem in syslems with distributed input delays is inherently finite dimensional. Syst and COntr Let 26:11–16MathSciNetzbMATHCrossRefGoogle Scholar
  22. 22.
    Tadmor G (1998) Robust control of systems with a single input lag In: Stability and Control of Time Lag Systems. LNClS-228. Springer Berlin New York LondonGoogle Scholar
  23. 23.
    Watanabe K, Ito M, (1981) An observer for linear feedback control laws of multivariable systems with multiple delays in controls and output. Syst and Contr Let 1:54–59zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Vladimir Răsvan
    • 1
  • Dan Popescu
    • 1
  1. 1.Department of Automatic ControlUniversity of CraiovaCraiovaROMANIA

Personalised recommendations