Necessary and sufficient stability condition of fractional-order interval linear systems

• Published in: Automatica (Oxford) Vol. 44; no. 11; pp. 2985 - 2988
• Main Authors: Ahn, Hyo-Sung, Chen, YangQuan
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.11.2008; Elsevier
• Subjects: Applied sciences; Computer science; control theory; systems; Control system analysis; Control theory. Systems; Exact sciences and technology; Fractional-order linear systems; Interval uncertainty; Necessary and sufficient stability condition; Interval uncertainty; Necessary and sufficient stability condition; Fractional-order linear systems; Robust stability; Necessary and sufficient condition; Hermitian matrix; Interval arithmetic; Fractional derivative; Robust control; Uncertain system; Polynomial interpolation; Interval matrix; Robustness; Lyapunov function
• ISSN: 0005-1098; 1873-2836
• DOI: 10.1016/j.automatica.2008.07.003

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 ≤ α < 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.