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Constructive Stabilization of Quadratic-Input Nonlinear Systems with Bounded Controls

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Abstract

In this paper, the stabilization of quadratic-input nonlinear systems with bounded controls is considered. According to the type of quadratic-input forms, two cases, namely, positive definite and positive semi-definite, are considered. For the case of positive definiteness, a universal formula for bounded stabilizers is given via a known Lyapunov control function. For the case of positive semidefiniteness, a constructive parametrization of bounded stabilizers is proposed under the assumption that there exists a known Lyapunov control function with respect to a smaller control set than the admissible control set.

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Authors and Affiliations

  1. Institute of Systems Science, Chinese Academy of Sciences, Beijing, 100080, P.R. China

    Jianghua Zhong & Daizhan Cheng

  2. Optimization and Systems Theory, Royal Institute of Technology, Stockholm, Sweden

    Xiaoming Hu

Authors
  1. Jianghua Zhong
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  2. Daizhan Cheng
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  3. Xiaoming Hu
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Corresponding author

Correspondence to Daizhan Cheng.

Additional information

This work is supported partly by NNSF of China under Grants 60221301 and 60334040, partly by Sida-VR Swedish Research Links Grant 348-2002-6936.

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Zhong, J., Cheng, D. & Hu, X. Constructive Stabilization of Quadratic-Input Nonlinear Systems with Bounded Controls. J Dyn Control Syst 14, 571–593 (2008). https://doi.org/10.1007/s10883-008-9052-x

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  • DOI: https://doi.org/10.1007/s10883-008-9052-x

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