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Nonlinear MIMO observable normal forms with output injection and output diffeomorphism

Author

Listed:
  • Liu, Jie
  • Boutat, Driss
  • Liu, Da-Yan
  • Zhang, Xue-Feng

Abstract

This research note establishes a specific framework for transforming nonlinear multi-input and multi-output diffeomorphism systems into extended observable normal forms without using differential geometry techniques. For this purpose, the nonlinear MIMO systems whose nonlinear terms do not need to be Lipschitz, are proposed. First, a change of coordinates is designed to eliminate the square items and coupled items for each nonlinear dynamical subsystem. Second, coupled auxiliary dynamics are constructed to transform the nonlinear multi-input and multi-output diffeomorphism systems into extended observable normal forms such that the finite-time and robust step-by-step sliding mode observer can be applied. Then, the state variables for the considered nonlinear dynamical systems are estimated by using the inverse of the transformations. Finally, the validity of the proposed design methods is verified by two numerical examples.

Suggested Citation

  • Liu, Jie & Boutat, Driss & Liu, Da-Yan & Zhang, Xue-Feng, 2025. "Nonlinear MIMO observable normal forms with output injection and output diffeomorphism," Applied Mathematics and Computation, Elsevier, vol. 489(C).
    • Handle: RePEc:eee:apmaco:v:489:y:2025:i:c:s0096300324006350
    DOI: 10.1016/j.amc.2024.129174
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    References listed on IDEAS

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    2. Angelo Alessandri, 2020. "Lyapunov Functions for State Observers of Dynamic Systems Using Hamilton–Jacobi Inequalities," Mathematics, MDPI, vol. 8(2), pages 1-14, February.
    3. Li, Ze & Ren, Junchao, 2024. "Adaptive event-triggered non-fragile sliding mode control for uncertain T-S fuzzy singular systems with passive constraint," Applied Mathematics and Computation, Elsevier, vol. 472(C).
    4. Jun Zhou & Xianqiang Li, 2015. "Finite-Time Sliding Mode Control Design for Unknown Nonaffine Pure-Feedback Systems," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-9, September.
    5. Xian-Ming Zhang & Qing-Long Han & Xiaohua Ge, 2022. "The construction of augmented Lyapunov-Krasovskii functionals and the estimation of their derivatives in stability analysis of time-delay systems: a survey," International Journal of Systems Science, Taylor & Francis Journals, vol. 53(12), pages 2480-2495, September.
    6. Alejandro F. Villaverde, 2019. "Observability and Structural Identifiability of Nonlinear Biological Systems," Complexity, Hindawi, vol. 2019, pages 1-12, January.
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