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More relaxed non-quadratic stabilization conditions for TS fuzzy control systems using LMI and GEVP

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  • Intelligent and Information Systems
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Abstract

In this paper, a new systematic approach is presented to further decrease the conservativeness in stability analysis condition and controller design. Non-quadratic Lyapunov function is utilized to derive stability conditions in terms of linear matrix inequalities. Also, the control problem is formulated in a generalized eigenvalue problem. Considering the concept of decay rate and control input constraint, a new systematic procedure is proposed to calculate a maximum bound for the upper bounds of the time derivatives of the membership functions. Moreover, some slack matrices are introduced that help to reduce conservativeness. The number of inequalities is few compared to the existing results in literature, which helps the feasibility in the case of large number of fuzzy rules. Simulation examples and comparison results demonstrate the merits of this method.

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Authors and Affiliations

  1. Control Eng. Dept., Electrical and Electronics Eng. Faculty, Shiraz University of Technology, Shiraz, Fars Province, Iran

    Navid Vafamand & Mokhtar Sha Sadeghi

Authors
  1. Navid Vafamand
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  2. Mokhtar Sha Sadeghi
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Correspondence to Mokhtar Sha Sadeghi.

Additional information

Recommended by Associate Editor Myung Geun Chun under the direction of Editor-in-Chief Young Hoon Joo.

Navid Vafamand received his B.S. and M.S. degrees from the Electrical Engineering Department, Shiraz University of Technology, Shiraz, Iran, in 2012 and 2014, respectively. His research interests include fuzzy model based control, LMI and adaptive control.

Mokhtar Sha Sadeghi received his B.S. degree in Electronics Engineering from Shiraz University, Shiraz in 1996, and his M.Sc. and Ph.D. degrees from Tarbiat Modares University, in 2001 and 2007, respectively, all in Iran. His research interests include robust control, adaptive control, fuzzy control, time delay systems, optimization, LMI, and neural networks.

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Vafamand, N., Sha Sadeghi, M. More relaxed non-quadratic stabilization conditions for TS fuzzy control systems using LMI and GEVP. Int. J. Control Autom. Syst. 13, 995–1002 (2015). https://doi.org/10.1007/s12555-013-0497-7

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  • DOI: https://doi.org/10.1007/s12555-013-0497-7

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