LMI optimization problem of delay-dependent robust stability criteria for stochastic systems with polytopic and linear fractional uncertainties

Pagavathigounder Balasubramaniam; Shanmugam Lakshmanan; Rajan Rakkiyappan

International Journal of Applied Mathematics and Computer Science (2012)

  • Volume: 22, Issue: 2, page 339-351
  • ISSN: 1641-876X

Abstract

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This paper studies an LMI optimization problem of delay-dependent robust stability criteria for stochastic systems with polytopic and linear fractional uncertainties. The delay is assumed to be time-varying and belong to a given interval, which means that lower and upper bounds of this interval time-varying delay are available. The uncertainty under consideration includes polytopic-type uncertainty and linear fractional norm-bounded uncertainty. Based on the new Lyapunov-Krasovskii functional, some inequality techniques and stochastic stability theory, delay-dependent stability criteria are obtained in terms of Linear Matrix Inequalities (LMIs). Moreover, the derivative of time delays is allowed to take any value. Finally, four numerical examples are given to illustrate the effectiveness of the proposed method and to show an improvement over some results found in the literature.

How to cite

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Pagavathigounder Balasubramaniam, Shanmugam Lakshmanan, and Rajan Rakkiyappan. "LMI optimization problem of delay-dependent robust stability criteria for stochastic systems with polytopic and linear fractional uncertainties." International Journal of Applied Mathematics and Computer Science 22.2 (2012): 339-351. <http://eudml.org/doc/208112>.

@article{PagavathigounderBalasubramaniam2012,
abstract = {This paper studies an LMI optimization problem of delay-dependent robust stability criteria for stochastic systems with polytopic and linear fractional uncertainties. The delay is assumed to be time-varying and belong to a given interval, which means that lower and upper bounds of this interval time-varying delay are available. The uncertainty under consideration includes polytopic-type uncertainty and linear fractional norm-bounded uncertainty. Based on the new Lyapunov-Krasovskii functional, some inequality techniques and stochastic stability theory, delay-dependent stability criteria are obtained in terms of Linear Matrix Inequalities (LMIs). Moreover, the derivative of time delays is allowed to take any value. Finally, four numerical examples are given to illustrate the effectiveness of the proposed method and to show an improvement over some results found in the literature.},
author = {Pagavathigounder Balasubramaniam, Shanmugam Lakshmanan, Rajan Rakkiyappan},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {delay-dependent stability; linear matrix inequality; Lyapunov-Krasovskii functional; stochastic systems},
language = {eng},
number = {2},
pages = {339-351},
title = {LMI optimization problem of delay-dependent robust stability criteria for stochastic systems with polytopic and linear fractional uncertainties},
url = {http://eudml.org/doc/208112},
volume = {22},
year = {2012},
}

TY - JOUR
AU - Pagavathigounder Balasubramaniam
AU - Shanmugam Lakshmanan
AU - Rajan Rakkiyappan
TI - LMI optimization problem of delay-dependent robust stability criteria for stochastic systems with polytopic and linear fractional uncertainties
JO - International Journal of Applied Mathematics and Computer Science
PY - 2012
VL - 22
IS - 2
SP - 339
EP - 351
AB - This paper studies an LMI optimization problem of delay-dependent robust stability criteria for stochastic systems with polytopic and linear fractional uncertainties. The delay is assumed to be time-varying and belong to a given interval, which means that lower and upper bounds of this interval time-varying delay are available. The uncertainty under consideration includes polytopic-type uncertainty and linear fractional norm-bounded uncertainty. Based on the new Lyapunov-Krasovskii functional, some inequality techniques and stochastic stability theory, delay-dependent stability criteria are obtained in terms of Linear Matrix Inequalities (LMIs). Moreover, the derivative of time delays is allowed to take any value. Finally, four numerical examples are given to illustrate the effectiveness of the proposed method and to show an improvement over some results found in the literature.
LA - eng
KW - delay-dependent stability; linear matrix inequality; Lyapunov-Krasovskii functional; stochastic systems
UR - http://eudml.org/doc/208112
ER -

References

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