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Sep.  2019

IEEE/CAA Journal of Automatica Sinica

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Yufang Chang, Guisheng Zhai, Bo Fu and Lianglin Xiong, "Quadratic Stabilization of Switched Uncertain Linear Systems: A Convex Combination Approach," IEEE/CAA J. Autom. Sinica, vol. 6, no. 5, pp. 1116-1126, Sept. 2019. doi: 10.1109/JAS.2019.1911681
Citation: Yufang Chang, Guisheng Zhai, Bo Fu and Lianglin Xiong, "Quadratic Stabilization of Switched Uncertain Linear Systems: A Convex Combination Approach," IEEE/CAA J. Autom. Sinica, vol. 6, no. 5, pp. 1116-1126, Sept. 2019. doi: 10.1109/JAS.2019.1911681

Quadratic Stabilization of Switched Uncertain Linear Systems: A Convex Combination Approach

doi: 10.1109/JAS.2019.1911681
Funds:  This work was supported in part by the Japan Ministry of Education, Sciences and Culture under Grants-in-Aid for Scientific Research (C) (21560471), the Green Industry Leading Program of Hubei University of Technology (CPYF2017003), and the National Natural Science Foundation of China (11601474, 11461082)
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  • We consider quadratic stabilization for a class of switched systems which are composed of a finite set of continuoustime linear subsystems with norm bounded uncertainties. Under the assumption that there is no single quadratically stable subsystem, if a convex combination of subsystems is quadratically stable, then we propose a state-dependent switching law, based on the convex combination of subsystems, such that the entire switched linear system is quadratically stable. When the state information is not available, we extend the discussion to designing an output-dependent switching law by constructing a robust Luenberger observer for each subsystem.

     

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    Highlights

    • Quadratic stabilization is studied for a class of switched linear systems with norm bounded uncertainties.
    • A new concept “convex Hurwitz combination with L2 disturbance attenuation” is proposed for quadratic stabilization of switched uncertain linear systems.
    • When a convex combination of subsystems is quadratically stable, a state-dependent switching law is proposed such that the entire switched linear system is quadratically stable.
    • When a convex combination of subsystems is quadratically stable, and in addition a robust detectability condition holds for all subsystems, a robust Luenberger observer is constructed for each subsystem, and an output-dependent switching law is proposed to quadratically stabilize the switched uncertain linear system.
    • The feasibility of the convex combination condition, the switching law implementation and the associated observer can be checked by using standard LMI approach.

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