Some Results on the Qualitative Theory of Matrix †
نویسندگان
چکیده
In this paper, we discuss the sign stability and the potential stability for the linear time invarient system described by dx/dt=Ax, x∈Rn, A∈Rn×n. The necessary and sufficient conditions for sign stability are obtained. The sufficient conditions for potential stability are also discussed with the concept of cycle decomposition. The results obtained are more general than those so far known. The concept of inertia preservation, which is the generalization of sign stability, is introduced to classify matrices from the structural point of view. Some system structures to preserve inertia are shown.
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