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Control of Discrete 2-D Takagi–Sugeno Systems via a Sum-of-Squares Approach

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Abstract

The stabilization of Takagi–Sugeno systems is solved here for the two-dimensional polynomial discrete case, by using the sum-of-squares approach. First, we provide a stabilization condition formulated in terms of polynomial multiple Lyapunov functions. Then, a non-quadratic stabilization condition is developed by applying relaxed stabilization technique. Both conditions can be used for design, by solving them using numerical tools such as SOSTOOLS. A numerical example illustrates the effectiveness of the results.

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Acknowledgements

Prof. Fernando Tadeo is funded by Conserjería de Educación, Junta de Castilla y Leon with European Regional Development Funds (Grant No. CLU 2017-09 and UIC 233), and by Secretaría de Estado de Investigación, Desarrollo e Innovación (Grant No. DPI2014-54530-R).

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Authors and Affiliations

  1. LESSI, Department of Physics, Faculty of Sciences Dhar El Mehraz, B.P. 1796, Fes-Atlas, Morocco

    Redouane Chaibi, Abdelaziz Hmamed & El Houssaine Tissir

  2. Departamento de Ingenieria de Sistemas y Automatica, Institute of Sustainable Processes, Universidad de Valladolid, 47005, Valladolid, Spain

    Fernando Tadeo

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  1. Redouane Chaibi
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  2. Abdelaziz Hmamed
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  3. El Houssaine Tissir
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  4. Fernando Tadeo
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Correspondence to Fernando Tadeo.

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Chaibi, R., Hmamed, A., Tissir, E.H. et al. Control of Discrete 2-D Takagi–Sugeno Systems via a Sum-of-Squares Approach. J Control Autom Electr Syst 30, 137–147 (2019). https://doi.org/10.1007/s40313-018-00433-y

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