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Relaxed Sum-of-Squares Based Stabilization Conditions for Polynomial Fuzzy-Model-Based Control Systems

Journal Article


Abstract


  • This paper presents a relaxed stabilization condition for polynomial-fuzzy-model-based control system by using sum-of-squares (SOS) approach. Full-block S-procedure is utilized to equivalently decouple the fuzzy weighting constraint into two constraints, which can be computed directly with the SOS approach. Besides, a free full-block multiplier imposed by this procedure also contributes to reducing the conservativeness of stability analysis. The copositivity verification relaxation performed on the membership-functions-related constraint can both obtain more relaxed results and reduce the computation complexity. The concept of polynomial Lyapunov function (PLF) with square matrical representation, which simplifies the stabilization condition by avoiding partial derivatives of a polynomial matrix, is also introduced to generalize the existing expression of PLFs. Then, the derived stabilization condition, which is represented in terms of SOS can be numerically solved. Three simulation examples are conducted to illustrate the effectiveness and applicability of the proposed method. These examples also demonstrate the advantages of the proposed method over the existing convex SOS approach.

Publication Date


  • 2019

Citation


  • Zhao, Y., He, Y., Feng, Z., Shi, P., & Du, X. (2019). Relaxed Sum-of-Squares Based Stabilization Conditions for Polynomial Fuzzy-Model-Based Control Systems. IEEE Transactions on Fuzzy Systems, 27(9), 1767-1778. doi:10.1109/TFUZZ.2018.2889019

Scopus Eid


  • 2-s2.0-85058903344

Web Of Science Accession Number


Start Page


  • 1767

End Page


  • 1778

Volume


  • 27

Issue


  • 9

Abstract


  • This paper presents a relaxed stabilization condition for polynomial-fuzzy-model-based control system by using sum-of-squares (SOS) approach. Full-block S-procedure is utilized to equivalently decouple the fuzzy weighting constraint into two constraints, which can be computed directly with the SOS approach. Besides, a free full-block multiplier imposed by this procedure also contributes to reducing the conservativeness of stability analysis. The copositivity verification relaxation performed on the membership-functions-related constraint can both obtain more relaxed results and reduce the computation complexity. The concept of polynomial Lyapunov function (PLF) with square matrical representation, which simplifies the stabilization condition by avoiding partial derivatives of a polynomial matrix, is also introduced to generalize the existing expression of PLFs. Then, the derived stabilization condition, which is represented in terms of SOS can be numerically solved. Three simulation examples are conducted to illustrate the effectiveness and applicability of the proposed method. These examples also demonstrate the advantages of the proposed method over the existing convex SOS approach.

Publication Date


  • 2019

Citation


  • Zhao, Y., He, Y., Feng, Z., Shi, P., & Du, X. (2019). Relaxed Sum-of-Squares Based Stabilization Conditions for Polynomial Fuzzy-Model-Based Control Systems. IEEE Transactions on Fuzzy Systems, 27(9), 1767-1778. doi:10.1109/TFUZZ.2018.2889019

Scopus Eid


  • 2-s2.0-85058903344

Web Of Science Accession Number


Start Page


  • 1767

End Page


  • 1778

Volume


  • 27

Issue


  • 9