Decay rate constrained stability analysis for positive systems with discrete and distributed delays

This paper is concerned with the decay rate constrained exponential stability analysis for continuous-time positive systems with both time-varying discrete and distributed delays. A necessary and sufficient condition is first given to ensure that a positive system with distributed delay is exponentially stable and satisfies a prescribed decay rate. Furthermore, by exploiting the monotonicity of the trajectory of a constant delay system and comparing the trajectory of the time-varying delay system with that of the constant delay system, the results are extended to positive systems with both bounded time-varying discrete delays and distributed delays.