Ultimate boundedness theorem for model reference adaptive control systems

This paper presents a novel formulation of the Lyapunov-based ultimate boundedness theorem with explicit specification of transient and ultimate bounds, time to the ultimate bound, and the set of admissible initial conditions. The formulation is tailored to the structure of model reference adaptive control systems accounting for a partitioning of the state vector into a tracking error and a parameter estimation error. It allows for a computation of separate bounds for the single state vector partitions in favor of a single bound on the compound state, consisting of both partitions. This is of great practical importance because tracking error and parameter estimation error are of different magnitudes in general. Regarding model reference adaptive control systems, it is the state of the technology so far that the ultimate boundedness theorem is tailored to the structure of the considered system each time, again and again. It is hence manifest to formulate once a generic version of the theorem, tailored to model reference adaptive control systems, but not to reinvent the wheel for each case.