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Global stabilization of linear systems with bounded controls using state-dependent saturation functions

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Abstract

By using the so-called SP-stable polynomials, this paper reconsiders the problem of global stabilization of linear systems with input saturation. Firstly, a new nonlinear feedback law consisting of parallel connections of saturation functions by means of the so-called state-dependent saturation function is proposed for global stabilization of chains of integrators system. The state-dependent saturation function allows increasing the control energy when some of the states are badly scaled and can improve significantly the transient performances of the closed-loop system. Secondly, this type of global stabilization nonlinear feedback laws is extended to a class of linear systems that can be globally stabilized by bounded controls. Numerical examples show the effectiveness of the proposed approach.

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Authors and Affiliations

  1. Center for Control Theory and Guidance Technology, Harbin Institute of Technology, Harbin, 150001, China

    Bin Zhou, Guangren Duan & He Kong

Authors
  1. Bin Zhou
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  2. Guangren Duan
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  3. He Kong
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Corresponding author

Correspondence to Bin Zhou.

Additional information

This work was supported in part by the National Natural Science Foundation of China under Grant Nos. 60904007 and 61074111, the China Postdoctoral Science Foundation under Grant No. 20100480059, the Heilongjiang Postdoctoral Foundation of China under Grant No. LRB10-194, the Foundation for Innovative Research Group of the National Natural Science Foundation of China under Grant No. 601021002, and the Development Program for Outstanding Young Teachers at the Harbin Institute of Technology under Grant No. HITQNJS.2009.054.

This paper was recommended for publication by Editor Jifeng ZHANG.

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Zhou, B., Duan, G. & Kong, H. Global stabilization of linear systems with bounded controls using state-dependent saturation functions. J Syst Sci Complex 24, 477–490 (2011). https://doi.org/10.1007/s11424-011-8325-8

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  • DOI: https://doi.org/10.1007/s11424-011-8325-8

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