An efficient algorithm for estimating dynamical integrity in time-delay systems

In nonlinear systems, the dynamical integrity of a steady state solution characterizes its robustness against external perturbations. Determining the dynamical integrity is a challenging task even for moderately sized systems, and it becomes even more complex in time-delay systems due to their infinite-dimensional state-space representation. Building upon previous studies, the current paper targets this problem and introduces an efficient iterative algorithm for estimating the local integrity measure of both fixed points and limit cycles in time-delay systems. The proposed method is computationally fast, enabling parametric analysis and making it a powerful tool for identifying safety-critical parameter regions, where even small disturbances can cause the system to escape the desired steady state. The effectiveness of the algorithm is demonstrated through two case studies: a delayed van der Pol–Duffing oscillator and an inverted pendulum equipped with a tuned vibration absorber. • Dynamical integrity estimation algorithm is developed. • The algorithm works for time delay systems. • The algorithm is significantly faster than other methods. • The algorithm is validated on two dynamical systems.