Robust direct adaptive control for a class of systems with delays

This paper presents a direct adaptive control algorithm, based on a σ-modification rule, which is robust with respect to additive and multiplicative plant unmodelled dynamics for plants involving both internal and external known point delays. Several adaptive controller structures are given and analyzed for the case of plants with unknown parameters while being assumed that the nominal plant is of known order and relative order. The parametrized parts of two of the controller structures involve delays while those of the two remaining controllers are delay-free. Auxiliary compensating signals which weight the plant input and output integrals are incorporated in all the controller structures for stabilization purposes. It is proved that, if the unmodelled dynamics is sufficiently small at low frequencies, then the adaptive algorithm guarantees boundedness of all the signals in the closed-loop system.