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A weighted switching sequence optimization algorithm for static output feedback control synthesis of nonlinear systems

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  • Gao, Jingjing
  • Xie, Xiangpeng

Abstract

In this paper, the static output feedback (SOF) control synthesis of discrete-time Takagi-Sugeno (T-S) fuzzy systems is concerned upon homogeneous polynomial parameter dependent Lyapunov functions (HPPD-LFs). It is well known that SOF control always leads to inequality conditions with non-convexity, which makes the optimization problem intractable. To overcome this difficulty, a novel switching sequence convex optimization (SSCO) algorithm is proposed, which is upon the matrix decomposition concept and the inner approximation strategy to eliminate the non-convex terms formed by the controller and the slack variables. Unlike conventional methods, the controller acts as a direct optimization variable and does not require structural or multiplicative relationships between the slack variables, which opens up the possibility of obtaining improved results in terms of l2 gain performance. In particular, more relaxed design conditions are obtained for SOF controller based on the weighted switching method by effectively utilizing the membership functions information. Finally, two simulation examples demonstrate the superiority of the developed SOF control scheme.

Suggested Citation

  • Gao, Jingjing & Xie, Xiangpeng, 2025. "A weighted switching sequence optimization algorithm for static output feedback control synthesis of nonlinear systems," Applied Mathematics and Computation, Elsevier, vol. 489(C).
    • Handle: RePEc:eee:apmaco:v:489:y:2025:i:c:s0096300324006131
    DOI: 10.1016/j.amc.2024.129152
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    References listed on IDEAS

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    1. Zhai, Ding & Lu, An-Yang & Dong, Jiuxiang & Zhang, Qing-Ling, 2017. "Stability analysis and state feedback control of continuous-time T–S fuzzy systems via anew switched fuzzy Lyapunov function approach," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 586-599.
    2. Ning, Jinghua & Hua, Changchun, 2022. "H∞ output feedback control for fractional-order T-S fuzzy model with time-delay," Applied Mathematics and Computation, Elsevier, vol. 416(C).
    3. Cherifi, Abdelmadjid & Guelton, Kevin & Arcese, Laurent & Leite, Valter J.S., 2019. "Global non-quadratic D-stabilization of Takagi–Sugeno systems with piecewise continuous membership functions," Applied Mathematics and Computation, Elsevier, vol. 351(C), pages 23-36.
    4. Ge, Chao & Liu, Zengshuai & Wang, Lei & Liu, Yajuan, 2022. "Improved stability criteria of T-S fuzzy systems with sampled-data-based dissipative control," Applied Mathematics and Computation, Elsevier, vol. 424(C).
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    6. Hu, Yue & Cai, Chenxiao & Lee, SeungHoon & Lee, YongGwon & Kwon, Oh-Min, 2023. "New results on H∞ control for interval type-2 fuzzy singularly perturbed systems with fading channel: The weighted try-once-discard protocol case," Applied Mathematics and Computation, Elsevier, vol. 448(C).
    7. Lee, Won Il & Park, Bum Yong & Kim, Sung Hyun, 2022. "Relaxed observer-based stabilization and dissipativity conditions of T-S fuzzy systems with nonhomogeneous Markov jumps via non-PDC scheme," Applied Mathematics and Computation, Elsevier, vol. 434(C).
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