Robust Simple Adaptive Control for Delayed Measurements Systems

In this paper an output-feedback problem is solved for a class of linear time delayed measurements systems with polytopic-type parameter uncertainties. The objective is to make the system output follow the output of a system model. The time-delay is either constant (known) or time-varying. In both cases, the problem is tackled by applying a combination of a simple direct adaptive control scheme, a Smith-predictor, and a low-pass filter. Sufficient conditions for closed-loop stability of the proposed control scheme are given, in terms of bilinear matrix inequalities. Two numerical examples are given, which demonstrate the applicability of the proposed methods and the simplicity of their implementation.