Time-delay margin computation of Model Reference Adaptive Control using the Razumikhin theorem

This paper deals with the computation of timedelay margins of state feedback Model Reference Adaptive Control (MRAC) with σ-modification for single input Linear Time Invariant (LTI) plants. Unlike previous results dealing with the computation of time-delay margins, a direct MRAC (without specific modification to accommodate for the time-delay) is considered in the tracking case. The time-delay margin is derived from the Lyapunov-Razumikhin proof of Uniform Ultimate Boundedness (UUB) of the delayed system. Key assumptions of the approach are the availability of known bounds for the tracking command and its derivative and the availability of known (conservative) bounds for the matched parametric uncertainties. Under these assumptions, UUB is established locally using a quadratic Lyapunov function. The satisfaction of the conditions of the Lyapunov-Razumikhin theorem is established using Sum-Of-Squares programming.