  We analyze stability properties of monotone nonlinear systems via
max-separable Lyapunov functions, motivated by the following observations:
first, recent results have shown that asymptotic stability of a monotone
nonlinear system implies the existence of a max-separable Lyapunov function on
a compact set; second, for monotone linear systems, asymptotic stability
implies the stronger properties of D-stability and insensitivity to
time-delays. This paper establishes that for monotone nonlinear systems,
equivalence holds between asymptotic stability, the existence of a
max-separable Lyapunov function, D-stability, and insensitivity to bounded and
unbounded time-varying delays. In particular, a new and general notion of
D-stability for monotone nonlinear systems is discussed and a set of necessary
and sufficient conditions for delay-independent stability are derived. Examples
show how the results extend the state-of-the-art.
