# 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

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topPagavathigounder 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 -

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