<abstract xml:lang="en" xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></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.

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

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

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

International Journal of Applied Mathematics and Computer Science

This paper studies an LMI optimization problem of delay-dependent robust stability criteria for stochastic systems with polytopic and linear fractional...

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

Published Online: Jun 28, 2012

Page range: 339 - 351

DOI: https://doi.org/10.2478/v10006-012-0025-6

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

This content is open access.

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

Published Online: Jun 28, 2012

Page range: 339 - 351

DOI: https://doi.org/10.2478/v10006-012-0025-6

Keywordsdelay-dependent stability, linear matrix inequality, Lyapunov-Krasovskii functional, stochastic systems

This content is open access.

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