Uncertainty estimation and cancellation for linear uncertain time-delay systems via adaptive memoryless control

This paper addresses the problem of estimating and cancelling uncertainty in a system when the uncertainty is known to be bounded, but its bound is unknown. Here, a class of linear uncertain time-delay systems, in which the uncertainty is an additive perturbation of a known (nominal) linear model, is studied. A novel, easy to implement, adaptive memoryless feedback control law, introduced in an `observer-like´ system, is designed to estimate the bounded uncertainty and this information is then used to cancel the effect of the uncertainty in the system. The main advantage is that, 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 only and not on the uncertain model.