Abstract
Following an idea originated by Conti for continuous matrix functions, an equivalence relation called summable similarity is defined on pairs of n × n matrix functions A and B. Special cases of the results show that if A and B are summably similar and the system (A) Δ x m = A m x m , m = 0, 1, 2, ... is uniformly, exponentially, or strictly stable, or has linear asymptotic equilibrium, then the system (B) Δ y m = B m y m , m = 0, 1, 2,... has the same property. More generally, the same conclusion is obtained under weaker conditions relating A and B.
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