Robust stability of some oscillatory systems including time-varying delay with applications in congestion control*

This paper focuses on the stability of some second-order linear systems with multiple constant and time-varying delays, under the assumption that the corresponding system without delays is an oscillator. Sufficient conditions for delay-dependent stability will be derived using the integral quadratic constraint approach combined with the generalized eigenvalue distribution of some appropriate finite-dimensional matrix pencils. As applications, we shall discuss some fluid approximation models used in congestion control of high-speed networks, under the natural assumptions that the control-time intervals are constant, but the round-trip times are time-varying.