Definition and Some Properties of Perron Stability

Abstract

The natural notions of Perron stability, Perron asymptotic stability, and Perron complete instability of the zero solution of a differential system are introduced. Peculiar features of these notions are noted in the one-dimensional, autonomous, and linear cases. Their connections with Perron exponents and with their counterparts in the sense of Lyapunov are described. The complete coincidence of the possibilities for studying the Perron and Lyapunov stability and asymptotic stability in the first approximation is revealed.