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International Journal of Applied Mathematics and Computer Science

The Journal of University of Zielona Gora and Lubuskie Scientific Society

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

Pagavathigounder Balasubramaniam1 / Shanmugam Lakshmanan1 / Rajan Rakkiyappan1

Department of Mathematics, Gandhigram Rural Institute-Deemed University, Gandhigram 624 302, Tamilnadu, India1

Department of Mathematics, Bharathiar University, Coimbatore 641 046, Tamilnadu, India2

This content is open access.

Citation Information: International Journal of Applied Mathematics and Computer Science. Volume 22, Issue 2, Pages 339–351, ISSN (Print) 1641-876X, DOI: 10.2478/v10006-012-0025-6, June 2012

Publication History

Published Online:
2012-06-28

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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