Abstract
This paper concerns the analysis of transferring stability properties from an invariant manifold to the whole space for an ordinary differential system. In previous papers we already treated this problem in the case of asymptotic and total stability. Here we deal with the case of non-asymptotic stability. We generalize to differential systems depending on time a reduction principle (Kelley in J Math Anal Appl 18:336–344, 1967; Pliss in Izv Akad Nauk SSSR Mat Ser 28:1297–1324, 1964) relative to autonomous systems. Our procedure is very different from the fixed point theorem argument used in Kelley (J Math Anal Appl 18:336–344, 1967), and it is based on the use of a suitable Liapunov function. Some results concerning integral stability are also given.
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