Adaptive memoryless controls for estimating uncertainty in linear uncertain systems with time-varying delays

An algorithm for an adaptive memoryless feedback control law, that is easy to implement in practice, is presented, which is designed to estimate bounded uncertainty in a class of linear uncertain time-delay systems. This estimated uncertainty is then used to cancel the effect of the uncertainty in the system so that it is then relatively straightforward to design `standard´ controllers in order to modify the behaviour of the uncertainty-free system. Here, a class of linear uncertain time-delay systems of the retarded type, in which the uncertainty is an additive perturbation of a known (nominal) linear model, is studied. The time-delays are assumed to be time-varying and unknown, but bounded. Thus, the main advantage of using this adaptive memoryless feedback control law is that the uncertainty can be cancelled from the system and, if further design objectives are to be realized (for example, with respect to a tracking problem), the controls can be designed on the information from the nominal model, i.e. the model without uncertainty, only, and not on the uncertain model.