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The robustness of dynamical systems against external perturbations is crucialin engineering; however, it is often overlooked for the lack of methods forrapidly computing it. This paper proposes a novel algorithm for estimating therobustness of systems subject to time delay. More precisely, the algorithmiteratively estimates the so-called local integrity measure (LIM), that is, theradius of the largest hypersphere centered at the fixed point and locatedwithin its basin of attraction. Since time-delayed systems are infinitedimensional, initial conditions are restricted to a constrained type of initialfunctions. The semi-discretization method is used for rapidly simulating thedynamics of the systems, while trajectories are classified as converging ordiverging using a subdivision of the reduced phase space into cells. Thealgorithm was tested on four different mechanical systems, and in all cases itvery quickly provided an accurate estimation of the LIM. Moreover, it enabledthe study of LIM trends in a multi-dimensional parameter space, which wouldhave been unfeasible with alternative methods. This breakthrough incomputational efficiency has important implications for engineering design,allowing for careful consideration of dynamical integrity and enhancing thesafety and reliability of engineered systems, especially in the presence oftime delays.

Dynamical integrity estimation in time delayed systems: a rapid iterative algorithm