© 1998 by Institute of Mathematics and its Applications
Robust direct adaptive control for a class of systems with delays
Departamento de Electricidad y Electrónica, Facultad de Ciencias, Universidad del Pais Vasco Apdo. 644. 48080 Bilbao (Leioa), Spain
This paper presents a direct adaptive control algorithm, based on a 
-modification rule, which is robust with respect to additive and multiplicative plant unmodelled dynamics for plants involing both internal (i.e. in the state) and external (i.e. in the output or input) Known point delays. A stabilizing adaptive controller structure is given and analysed for the case of a plant with unknown parameters, while it being assumed that the nominal plant is of known order and relative order. The parametrized part of the controller involves delays. Also, auxiliary compensating signals which weight the plant input and output integrals are incorporated for stabilization purposes. As a result, the adaptive controller is not designed based on signals over a ring, but signals having rational Laplace transforms are manipulated as well. 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 closedloop system.