Infinite-dimensional LMI approach to analysis and synthesis for linear time-delay systems

Kojiro Ikeda; Takehito Azuma; Kenko Uchida

Kybernetika (2001)

  • Volume: 37, Issue: 4, page [505]-520
  • ISSN: 0023-5954

Abstract

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This paper considers an analysis and synthesis problem of controllers for linear time-delay systems in the form of delay-dependent memory state feedback, and develops an Linear Matrix Inequality (LMI) approach. First, we present an existence condition and an explicit formula of controllers, which guarantee a prescribed level of L 2 gain of closed loop systems, in terms of infinite-dimensional LMIs. This result is rather general in the sense that it covers, as special cases, some known results for the cases of delay- independent/dependent and memoryless/memory controllers, while the infinity dimensionality of the LMIs makes the result difficult to apply. Second, we introduce a technique to reduce the infinite-dimensional LMIs to a finite number of LMIs, and present a feasible algorithm for synthesis of controllers based on the finite-dimensional LMIs.

How to cite

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Ikeda, Kojiro, Azuma, Takehito, and Uchida, Kenko. "Infinite-dimensional LMI approach to analysis and synthesis for linear time-delay systems." Kybernetika 37.4 (2001): [505]-520. <http://eudml.org/doc/33548>.

@article{Ikeda2001,
abstract = {This paper considers an analysis and synthesis problem of controllers for linear time-delay systems in the form of delay-dependent memory state feedback, and develops an Linear Matrix Inequality (LMI) approach. First, we present an existence condition and an explicit formula of controllers, which guarantee a prescribed level of $L^2$ gain of closed loop systems, in terms of infinite-dimensional LMIs. This result is rather general in the sense that it covers, as special cases, some known results for the cases of delay- independent/dependent and memoryless/memory controllers, while the infinity dimensionality of the LMIs makes the result difficult to apply. Second, we introduce a technique to reduce the infinite-dimensional LMIs to a finite number of LMIs, and present a feasible algorithm for synthesis of controllers based on the finite-dimensional LMIs.},
author = {Ikeda, Kojiro, Azuma, Takehito, Uchida, Kenko},
journal = {Kybernetika},
keywords = {time-delay system; linear system; LMI; time-delay system; linear system; LMI},
language = {eng},
number = {4},
pages = {[505]-520},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Infinite-dimensional LMI approach to analysis and synthesis for linear time-delay systems},
url = {http://eudml.org/doc/33548},
volume = {37},
year = {2001},
}

TY - JOUR
AU - Ikeda, Kojiro
AU - Azuma, Takehito
AU - Uchida, Kenko
TI - Infinite-dimensional LMI approach to analysis and synthesis for linear time-delay systems
JO - Kybernetika
PY - 2001
PB - Institute of Information Theory and Automation AS CR
VL - 37
IS - 4
SP - [505]
EP - 520
AB - This paper considers an analysis and synthesis problem of controllers for linear time-delay systems in the form of delay-dependent memory state feedback, and develops an Linear Matrix Inequality (LMI) approach. First, we present an existence condition and an explicit formula of controllers, which guarantee a prescribed level of $L^2$ gain of closed loop systems, in terms of infinite-dimensional LMIs. This result is rather general in the sense that it covers, as special cases, some known results for the cases of delay- independent/dependent and memoryless/memory controllers, while the infinity dimensionality of the LMIs makes the result difficult to apply. Second, we introduce a technique to reduce the infinite-dimensional LMIs to a finite number of LMIs, and present a feasible algorithm for synthesis of controllers based on the finite-dimensional LMIs.
LA - eng
KW - time-delay system; linear system; LMI; time-delay system; linear system; LMI
UR - http://eudml.org/doc/33548
ER -

References

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  12. Ikeda K., Azuma, T., Uchida K., A construction method of convex polyhedron in infinite number LMI approach for linear time-delay systems, In: Proc. of Annual Meeting of IEEJ 2000, pp. 1006–1007 (in Japanese) 
  13. Ikeda K., Uchida K., Analysis of state reachable sets for linear time-delay systems, In: Proc. of SICE2000, #105A-1 (in Japanese) 
  14. Lee J. H., Kim S. W., Kwon W. H., 10.1109/9.273356, IEEE Trans. Automat. Control 39 (1994), 159–162 (1994) MR1258692DOI10.1109/9.273356
  15. Li X., Souza C. E. de, LMI approach to delay-dependent robust stability and stabilization of uncertain linear delay systems, In: Proc. of Conference on Decision Control 1995, pp. 3614–3619 (1995) 
  16. Loiseau J. J., Brethe D., An effective algorithm for finite spectrum assignment of single input systems with delay, In: Proc. of Symposium Modeling, Analysis and Simulation, IEEE–IMACS Conference Computational Engineering in Systems Applications 1996 
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