This paper focuses on the global h-stability of the nonlinear positive system with multiple time-varying delays. Through differentiated expressions of the function h, the global h-stability could be referred to as several known stabilities, including Lagrange stability, asymptotic stability, global exponential stability, global practical stability, and so forth. By proposing a direct analysis method that differs from the so-called Lyapunov-Krasovskii functional method, we presented a sufficient condition for the global h-stability of such system. The obtained stability condition appeared in the form of a number of simple inequalities, which could be easily handled by the toolbox YALMIP loaded in MATLAB. The applicability of our results have been illustrated by three numerical examples. K E Y W O R D Sa direct analysis method, global h-stability, multiple time-varying delays, nonlinear time-varying positive systems

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