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Necessary and sufficient stability condition of fractional-order interval linear systems. (English) Zbl 1152.93455
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 1α<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:
93D09Robust stability of control systems