Stability of homogeneous positive systems with time-varying delays

Abstract

Stability analysis of positive linear systems has been well-developed, while attention to positive homogeneous nonlinear systems is notably less paid. This note deepens and extends some previous results on stability of homogeneous systems with bounded time-varying delays. Based on positivity property, exponential stability of a class of delayed homogeneous system with degree confined to an interval is studied, and its state boundary is further investigated in any fixed time, which is more precise than the former result in some cases. Additionally, finite-time stability is obtained for a delay-free homogeneous system and an explicit boundary is presented.