Zeros in linear systems with time delay in state

Jerzy Tokarzewski

International Journal of Applied Mathematics and Computer Science (2009)

  • Volume: 19, Issue: 4, page 609-617
  • ISSN: 1641-876X

Abstract

top
The concept of invariant zeros in a linear time-invariant system with state delay is considered. In the state-space framework, invariant zeros are treated as triples: complex number, nonzero state-zero direction, input-zero direction. Such a treatment is strictly related to the output-zeroing problem and in that spirit the zeros can be easily interpreted. The problem of zeroing the system output is discussed. For systems of uniform rank, the first nonzero Markov parameter comprises a certain amount of information concerning invariant zeros, output-zeroing inputs and zero dynamics. General formulas for output-zeroing inputs and zero dynamics are provided.

How to cite

top

Jerzy Tokarzewski. "Zeros in linear systems with time delay in state." International Journal of Applied Mathematics and Computer Science 19.4 (2009): 609-617. <http://eudml.org/doc/207959>.

@article{JerzyTokarzewski2009,
abstract = {The concept of invariant zeros in a linear time-invariant system with state delay is considered. In the state-space framework, invariant zeros are treated as triples: complex number, nonzero state-zero direction, input-zero direction. Such a treatment is strictly related to the output-zeroing problem and in that spirit the zeros can be easily interpreted. The problem of zeroing the system output is discussed. For systems of uniform rank, the first nonzero Markov parameter comprises a certain amount of information concerning invariant zeros, output-zeroing inputs and zero dynamics. General formulas for output-zeroing inputs and zero dynamics are provided.},
author = {Jerzy Tokarzewski},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {linear systems; time delay in state; state-space methods; output-zeroing problem; invariant zeros},
language = {eng},
number = {4},
pages = {609-617},
title = {Zeros in linear systems with time delay in state},
url = {http://eudml.org/doc/207959},
volume = {19},
year = {2009},
}

TY - JOUR
AU - Jerzy Tokarzewski
TI - Zeros in linear systems with time delay in state
JO - International Journal of Applied Mathematics and Computer Science
PY - 2009
VL - 19
IS - 4
SP - 609
EP - 617
AB - The concept of invariant zeros in a linear time-invariant system with state delay is considered. In the state-space framework, invariant zeros are treated as triples: complex number, nonzero state-zero direction, input-zero direction. Such a treatment is strictly related to the output-zeroing problem and in that spirit the zeros can be easily interpreted. The problem of zeroing the system output is discussed. For systems of uniform rank, the first nonzero Markov parameter comprises a certain amount of information concerning invariant zeros, output-zeroing inputs and zero dynamics. General formulas for output-zeroing inputs and zero dynamics are provided.
LA - eng
KW - linear systems; time delay in state; state-space methods; output-zeroing problem; invariant zeros
UR - http://eudml.org/doc/207959
ER -

References

top
  1. Bourles, H. and Fliess, M. (1997). Finite poles and zeros of linear systems: An intrinsic approach, International Journal of Control 68(4):897-922. Zbl1034.93009
  2. Górecki, H., Fuksa, S., Grabowski, P. and Korytowski, A. (1989). Analysis and Synthesis of Time Delay Systems, PWN/Wiley, Warsaw/Chichester. Zbl0695.93002
  3. Hale, J. (1977). Theory of Functional Differential Equations, Springer, New York, NY. Zbl0352.34001
  4. Isidori, A. (1995). Nonlinear Control Systems, Springer Verlag, London. Zbl0878.93001
  5. Kamen, E. W., Khargonekar, P. P. and Tannenbaum, A. (1985). Stabilization of time-delay systems using finitedimensional compensators, IEEE Transactions on Automatic Control 30(1): 75-78. Zbl0557.93052
  6. Kharitonov, V. L. (1999). Robust stability analysis of time delay systems: A survey, Annual Reviews in Control 23(1): 185-196. 
  7. Kharitonov V. L. and Hinrichsen, D. (2004). Exponential estimates for time delay systems, Systems and Control Letters 53(5):395-405. Zbl1157.34355
  8. Lee, E. B. and Olbrot, A. W. (1981). Observability and related structural results for linear hereditary systems, International Journal of Control 34(6):1061-1078. Zbl0531.93015
  9. MacFarlane, A. G. J. and Karcanias, N. (1976). Poles and zeros of linear multivariable systems: A survey of the algebraic, geometric and complex variable theory, International Journal of Control 24(1):33-74. Zbl0374.93014
  10. Marro, G. (1996). Multivariable regulation in geometric terms: Old and new results, in C. Bonivento, G. Marro, R. Zanasi (Eds.), Colloquium on Automatic Control, Lecture Notes in Control and Information Sciences, Vol. 215, Springer Verlag, London, pp. 77-138. Zbl0890.93021
  11. Pandolfi, L. (1982). Transmission zeros of systems with delays, International Journal of Control 36(6): 959-976. Zbl0504.93026
  12. Pandolfi, L. (1986). Disturbance decoupling and invariant subspaces for delay systems, Applied Mathematics and Optimization 14(1): 55-72. Zbl0587.93039
  13. Richard, J. P. (2003). Time-delay systems: An overview of some recent advances and open problems, Automatica 39(10): 1667-1694. Zbl1145.93302
  14. Schrader, C. B. and Sain, M. K. (1989). Research on system zeros: A survey, International Journal of Control 50(4):1407-1433. Zbl0686.93036
  15. Sontag, E. D. (1990). Mathematical Control Theory, Springer Verlag, New York, NY. Zbl0703.93001
  16. Tokarzewski, J. (2002). Zeros in Linear Systems: A Geometric Approach, Warsaw University of Technology Press, Warsaw. Zbl1044.93036
  17. Tokarzewski, J. (2006). Finite Zeros in Discrete-Time Control Systems, Lecture Notes in Control and Information Sciences, Vol. 338, Springer Verlag, Berlin. Zbl1203.93118

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.