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Research articles

ScienceAsia 45 (2019): 172-178 |doi: 10.2306/scienceasia1513-1874.2019.45.172

A new necessary and sufficient condition for the simultaneous stabilization of three time-varying linear systems

Liu Liu*, Lu Yufeng

ABSTRACT:     This paper considers the simultaneous stabilization problems of three discrete-time time-varying linear systems within the framework of nest algebra. Under the transmission condition, a necessary and sufficient condition for the existence of simultaneously stabilizing controllers is given based on the strong representation. Some simultaneous stabilizability criteria are established in terms of single strong representation of only one controller in the transmission condition.

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a School of Mathematical Sciences, Dalian University of Technology, Dalian 116024 China

* Corresponding author, E-mail: beth.liu@dlut.edu.cn

Received 4 May 2018, Accepted 26 Apr 2019