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Simultaneous stabilization of a class of nonlinear descriptor systems via Hamiltonian function method

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Abstract

This paper studies simultaneous stabilization of a class of nonlinear descriptor systems via the Hamiltonian function method. Firstly, based on the Hamiltonian realization of the nonlinear descriptor systems and a suitable output feedback, two nonlinear descriptor systems are equivalently transformed into two nonlinear Hamiltonian differential-algebraic systems by a nonsingular transformation, and a sufficient condition for two closed-loop systems to be impulse-free is given. The two systems are then combined to generate an augmented dissipative Hamiltonian differential-algebraic system by using the system-augmentation technique, based on which a simultaneous stabilization controller and a robust simultaneous stabilization controller are designed for the two systems. Secondly, the case of more than two nonlinear descriptor systems is investigated, and two new results are proposed for the simultaneous stabilization and robust simultaneous stabilization, respectively. Finally, an illustrative example is studied by using the results proposed in this paper, and simulations show that the simultaneous stabilization controllers obtained in this paper work very well.

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Authors and Affiliations

  1. School of Control Science and Engineering, Shandong University, Jinan, 250061, China

    LiYing Sun & YuZhen Wang

  2. School of Science, University of Jinan, Jinan, 250022, China

    LiYing Sun

Authors
  1. LiYing Sun
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  2. YuZhen Wang
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Correspondence to LiYing Sun.

Additional information

Supported by the National Natural Science Foundation of China (Grant No. 60774009), the Natural Science Foundation of Shandong Province (Grant No. Y2006G10), and the Research Fund for the Doctoral Program of Chinese Higher Education (Grant No. 200804220028)

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Sun, L., Wang, Y. Simultaneous stabilization of a class of nonlinear descriptor systems via Hamiltonian function method. Sci. China Ser. F-Inf. Sci. 52, 2140–2152 (2009). https://doi.org/10.1007/s11432-009-0181-y

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  • DOI: https://doi.org/10.1007/s11432-009-0181-y

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