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Volume 6 Issue 5
Sep.  2019

IEEE/CAA Journal of Automatica Sinica

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Article Contents
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.

# 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)
• 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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