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Finite-time stabilization via output feedback for high-order planar systems subjected to an asymmetric output constraint

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Abstract

This article addresses the problem of finite-time stabilization via output feedback for high-order planar systems subjected to an asymmetric output constraint. By delicately exploring the features of nonlinearities and utilizing skillful manipulations of signum functions, a new fraction-type asymmetric barrier Lyapunov function and a distinctive non-smooth state observer are developed. On the basis of the proposed barrier Lyapunov function along with the state observer, the celebrated adding a power integrator technique is elegantly renovated to develop a novel approach by which a continuous output feedback finite-time stabilizer is constructed in a systematic fashion while ensuring the fulfillment of a pre-specified asymmetric output constraint. The presented scheme is a unification approach able to achieve the finite-time stabilization via output feedback for systems subjected to or free from output constraints simultaneously, without needing to change both the controller and observer structures. A numerical is provided to illustrate the superiority of the developed method.

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Notes

  1. That is, \(\eta (t)\) is a maximal solution (for the definition, see [33]) defined on \([t_0,\infty )\).

  2. For any \(\eta (t_0)\in {\mathbb {M}}_n(\kappa _l,\kappa _u)\), the solution of system (2) is in general not unique because \(f(\eta ,t)\) is only continuous [33].

  3. \({\dot{V}}_1(x_1):=( \partial V_1(x_1)/\partial x_1 ){\dot{x}}_1\) includes the variable \(x_2\) and the function \(\phi _1(x_1,t)\); thus, it is directly related to \((x,t)\in {\mathbb {M}}_2(\kappa _l,\kappa _u)\times {\mathbb {R}}^+\).

  4. We adapt the fact that any real-valued continuous function has a nonnegative smooth upper bound function (see, e.g., [36, Theorem 6.21, p. 136]).

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Acknowledgements

This work was supported in part by the Ministry of Science and Technology (MOST), Taiwan, under Grant MOST 109-2221-E-006-089-.

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Authors and Affiliations

  1. Department of Systems and Naval Mechatronic Engineering, National Cheng Kung University, Tainan, 70101, Taiwan

    Chih-Chiang Chen & Guan-Shiun Chen

  2. Institute of Automation, Qufu Normal University, Qufu, 273165, Shandong Province, China

    Zong-Yao Sun

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  1. Chih-Chiang Chen
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Correspondence to Chih-Chiang Chen.

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Chen, CC., Chen, GS. & Sun, ZY. Finite-time stabilization via output feedback for high-order planar systems subjected to an asymmetric output constraint. Nonlinear Dyn 104, 2347–2361 (2021). https://doi.org/10.1007/s11071-021-06402-6

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