$\mu $ -Stability of Nonlinear Positive Systems With Unbounded Time-Varying Delays.

Abstract

The stability of the zero solution plays an important role in the investigation of positive systems. In this brief, we discuss the μ -stability of positive nonlinear systems with unbounded time-varying delays. The system is modeled by the continuous-time ordinary differential equation. Under some assumptions on the nonlinear functions, such as homogeneous, cooperative, and nondecreasing, we propose a novel transform, by which the nonlinear system reduces to a new system. Thus, we analyze its dynamics, which can simplify the nonlinear homogenous functions with respect to the arbitrary dilation map to those with respect to the standard dilation map. We finally get some new criteria for the global μ -stability taking the degree into consideration. A numerical example is given to demonstrate the validity of obtained results.