Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-25T23:48:20.614Z Has data issue: false hasContentIssue false
  • English
  • Français

Robust stability analysis of a class of uncertain neutral T–S fuzzy systems with time delay

Published online by Cambridge University Press:  04 September 2014

YANJIANG LI ,
CHONG TAN ,
JIANTING LV  and
XIAN ZHANG
YANJIANG LI
Affiliation:
School of Mathematical Science, Heilongjiang University, Harbin 150080, China Email: [email protected]; [email protected]; [email protected]
CHONG TAN
Affiliation:
School of Automation, Harbin University of Science and TechnologyHarbin 150080, China Email: [email protected]
JIANTING LV
Affiliation:
School of Mathematical Science, Heilongjiang University, Harbin 150080, China Email: [email protected]; [email protected]; [email protected]
XIAN ZHANG
Affiliation:
School of Mathematical Science, Heilongjiang University, Harbin 150080, China Email: [email protected]; [email protected]; [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider the problem of the robust stability of a class of uncertain T–S fuzzy neutral systems with time delay under time-varying parametric uncertainties using the Lyapunov–Krasovskii approach, where the parametric uncertainty is assumed to be norm bounded. By choosing a new Lyapunov–Krasovskii function, we are able to propose less conservative robust stability criteria in terms of linear matrix inequalities (LMIs) such that the uncertain T–S fuzzy neutral system under consideration remains asymptotically stable. The reduced conservatism of the proposed stability criterion compared with recently reported results is attributed to our using the Jensen inequality. The obtained results can also reduce the computational complexity.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 24 , Special Issue 5: Mathematical Method in Intelligent Computing and Automation , October 2014 , e240521
Copyright
Copyright © Cambridge University Press 2014 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Brayton, R. K. (1966) Bifurcation of periodic solutions in a nonlinear difference-differential equation of neutral type. Quarterly of Applied Mathematics 24 215–224.CrossRefGoogle Scholar
Cao, Y. Y., Sun, Y. X. and Lam, J. (1998) Delay-dependent robust control for uncertain systems with time-varying delays. IEE Proceedings on Control Theory Applications 145 (3)338–344.Google Scholar
Chen, B., Liu, X.P, Zhou, Y. and Li, H. (2005) Fuzzy guaranteed cost control for nonlinear systems with time-varying delay. IEEE Transactions on Fuzzy Systems 13 (2)238–249.CrossRefGoogle Scholar
Gu, K. (2000) An integral inequality in the stability problem of time-delay systems. In Proceedings of the 39th IEEE Conference Decision Control 1077–1081.Google Scholar
He, Y., Wang, Q.G, Wu, M. and Lin, C. (2006) Delay-dependent state estimation for delay neural networks. IEEE Transactions on Neural Networks 17 (4)1077–1081.Google Scholar
Kuang, Y. (1993) Delay Differential Equations with Applications in Population Dynamics, Academic Press.Google Scholar
Li, Y. and Xu, S. (2008) Robust stabilization and control for uncertain fuzzy neutral systems with mixed time delays. Fuzzy Sets and Systems 159 2730–2748.Google Scholar
Liang, J., Wang, Z. and Liu, X. (2010) Robust passivity and passification of stochastic fuzzy time-delay systems. Information Sciences 180 1725–1737.Google Scholar
Liu, L. L., Zhang, Q. L. and Du, Z. P. (2009) Stability of the singular networked control systems with time-delay and data packet dropout. Journal of Northeastern University 30 (3)318–320.Google Scholar
MahmoudM, S. M, S. (2009) Generalized H∞ control of switched discrete-time systems with unknown delays. Applied Mathematics and Computation 211 (1)33–44.Google Scholar
Song, B., Xu, Y. and Zou, Y. (2009) Delay-dependent robust filtering for uncertain neutral stochastic time-delay systems. Circuits, Systems, and Signal Processing 28 (2)241–256.Google Scholar
Takagi, T. and Sugeno, M. (1985) Fuzzy identification of systems and its applications to modeling and control. IEEE Transactions on System, Man, Cybernetics 15 116–132.Google Scholar
Tian, E. Q., Yue, D. and Zhang, Y. J. (2009) Delay-dependent robust control for T–S fuzzy system with time-varing delay. Fuzzy Sets and Systems 160 (12)1708–1719.CrossRefGoogle Scholar
Wang, H. O., Takagi, K. and Griffin, M. F. (1996) An approach to fuzzy control of nonlinear systems: stability and design issues. IEEE Transactions on Fuzzy Systems 4 (1)14–23.Google Scholar
Xu, S., Lam, J. and Chen, B. (2004) Robust H∞ control for uncertain fuzzy neutral delay systems. International Journal of Robust Nonlinear Control 15 233–246.Google Scholar
Xu, S., Lam, J. and Zou, Y. (2005) Further results on delay-dependent robust stability conditions of uncertain neutral systems. European Journal of Control 10 365–380.Google Scholar
Yang, J., Luo, W., Li, G. and Zhong, S. (2010) Reliable guaranteed cost control for uncertain fuzzy neutral systems. Nonlinear Analysis: Hybrid Systems 4 644–658.Google Scholar
Yang, J., Zhong, S., Li, G. and Luo, W. (2009) Robust H∞ filter design for uncertain fuzzy neutral systems. Information Science 179 3697–3710.Google Scholar
Zadeh, L. A. (1965) Fuzzy sets. Information Control 8 338–353.CrossRefGoogle Scholar
Zhang, X. M., Wu, M.She, J. H. and He, Y. (2005) Delay-dependent stabilization of linear systems with state and input delays. Automatica 41 (8)1405–1412.Google Scholar