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Zbl 1152.93455
Ahn, Hyo-Sung; Chen, Yangquan
Necessary and sufficient stability condition of fractional-order interval linear systems. (English)
[J] Automatica 44, No. 11, 2985-2988 (2008). ISSN 0005-1098

Summary: This paper establishes a necessary and sufficient stability condition of fractional-order interval linear systems. It is supposed that the system matrix $A$ is an interval uncertain matrix and fractional commensurate order belongs to $1\leq \alpha <2$. Using the existence condition of Hermitian $P=P^{*}$ for a complex Lyapunov inequality, we prove that the fractional-order interval linear system is robust stable if and only if there exists Hermitian matrix $P=P^{*}$ such that a certain type of complex Lyapunov inequality is satisfied for all vertex matrices. The results are directly extended to the robust stability condition of fractional-order interval polynomial systems.

MSC 2000:: *93D09 Robust stability of control systems

Keywords: fractional-order linear systems; interval uncertainty; necessary and sufficient stability condition

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Zentralblatt MATH Berlin [Germany]