delayssensitivity

Delayssensitivity is a concept used in control theory, signal processing, and networked systems to describe how a system’s performance responds to time delays in its signals. It captures the degree to which input delays, feedback delays, or communication delays affect stability, transient response, and steady-state behavior.

In linear time-invariant systems, a time delay tau typically appears as a factor e^{-s tau} in the transfer function, introducing phase lag that can degrade stability margins and alter dynamics. The delay sensitivity of a system can be quantified in several ways, such as the derivative of the closed-loop transfer function with respect to tau, or through normalized measures that relate changes in output to small changes in delay. Because the exact form depends on the system, practitioners often use general indicators like delay margins or the change in phase margin and gain margin as tau varies.

Common methods for analyzing delayssensitivity include Padé approximations to replace delays with rational functions, spectral or Nyquist analysis that accounts for delay-induced phase shifts, and numerical simulations that perturb delay to observe performance changes. In networked or distributed control, delayssensitivity helps assess robustness to communication latencies and scheduling variability, guiding the design of controllers and buffering strategies.

Applications and relevance include robotics, telecommunications, and industrial automation, where delays are inherent and can limit achievable performance. A key goal is to maximize delay margins or design controllers that maintain acceptable performance under expected delay ranges. See also time-delay systems, phase margin, delay margin, and sensitivity analysis.