Delay-independent global convergence in time-varying monotone systems of delay differential equations satisfying a scalability condition

Monotone systems generated by delay differential equations with explicit time-variation are of importance in the modeling of a number of significant practical problems, including the analysis of communication systems and consensus protocols. In such problems, it is often of importance to be able to guarantee delay-independent incremental global convergence, whereby all solutions converge towards each other asymptotically. Such guarantees allow the asymptotic properties of all trajectories of the system to be determined by simply studying those of some particular convenient solution. A class of these systems was recently studied in the context of wireless networks through the imposition of a scalability condition. In this work, we seek to weaken the notions of monotonicity and system structure that were employed in that setting so as to extend this analysis to a more general context and make explicit exactly which system properties are required. Furthermore, we obtain as a corollary a result of guaranteed convergence of all solutions to a quantifiable invariant set, enabling time-invariant asymptotic bounds to be obtained for the trajectories even if the precise values of time-varying parameters are unknown.