Abstract
This chapter deals with the problem of stabilization by state feedback control of Takagi–Sugeno (T–S) fuzzy discrete-time systems with multiple fixed delays while imposing positivity in closed-loop. The results are presented under the linear Programming (LP) form. In particular, the synthesis of state feedback controllers is first solved in terms of LP for unbounded control case. The obtained result is then extended to the stabilization problem by nonnegative control and stabilization by bounded control. The stabilization conditions are derived using the single Lyapunov–Krasovskii Functional (LKF). An example of a real plant is studied to show the advantages of the design procedure. To show the merit of the proposed method, a comparison between LP and LMI approaches is presented upon a second example.
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Benzaouia, A., El Hajjaji, A. (2014). Stabilization of Discrete-Time T–S Fuzzy Positive Systems with Multiple Delays. In: Advanced Takagi‒Sugeno Fuzzy Systems. Studies in Systems, Decision and Control, vol 8. Springer, Cham. https://doi.org/10.1007/978-3-319-05639-5_8
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DOI: https://doi.org/10.1007/978-3-319-05639-5_8
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