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The aim of the present work is for each complex matrix A ∈ C with spectral abscissa S(A) < 0 and for each vector norm ||.|| in C to establish an explicit construction to obtain a matrix measure μ||.|| with μ||.||(A) < 0. Furthermore the proved result is extended for the case when the entries ajk of the matrix A are continuous functions, i.e. a j k ∈ C(K,C), where K ⊂ C̄+ is an arbitrary compact set. AMS Subject Classification: 15A60, 37C75, 65F35

SOME INVERSE RESULTS ABOUT MATRIX STABILITY IN TERMS OF MATRIX MEASURE