Dependence and Independence of the Perron and Lyapunov Stability Properties on the System Phase Domain

Abstract

For a differential system, we study various properties related to Lyapunov and Perron stability. We prove that all of these properties are of specifically local nature. However, some of them may vary as the system phase domain shrinks, while the others remain unchanged. At the same time, the possibility of studying any of these properties by the first approximation is completely independent of the choice of the phase domain.