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International Journal of Applied Mathematics and Computer Science

Journal of University of Zielona Gora and Lubuskie Scientific Society

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Volume 22, Issue 2 (Jun 2012)

Issues

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

Pagavathigounder Balasubramaniam
  • Department of Mathematics, Gandhigram Rural Institute-Deemed University, Gandhigram 624 302, Tamilnadu, India
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Shanmugam Lakshmanan
  • Department of Mathematics, Gandhigram Rural Institute-Deemed University, Gandhigram 624 302, Tamilnadu, India
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Rajan Rakkiyappan
Published Online: 2012-06-28 | DOI: https://doi.org/10.2478/v10006-012-0025-6

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

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.

Keywords: delay-dependent stability; linear matrix inequality; Lyapunov-Krasovskii functional; stochastic systems

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About the article


Published Online: 2012-06-28

Published in Print: 2012-06-01


Citation Information: International Journal of Applied Mathematics and Computer Science, ISSN (Print) 1641-876X, DOI: https://doi.org/10.2478/v10006-012-0025-6.

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