Output-Feedback MRAC for Continuous State Delay Systems: the Relative Degree Two case

In this paper, model reference adaptive control (MRAC) of linear continuous-time state delay systems is presented with the assumption that the relative degree of the system without delay be two. Recently, a new two component controller structure was developed for state delay systems in which the relative degree of system without delay was assumed to be one. We have combined the two component controller structure with the well known Monopoli´s algorithm for systems with relative degree two, to extend the design for the relative degree two case. Closed-loop system stability and error convergence is proved by using a suitable Lyapunov-Krasovskii functional. The effectiveness of the theoretical results has been illustrated through simulation results.