Simple adaptive H∞ control for delayed measurements systems

An output-feedback direct adaptive control problem is considered for a class of linear time delayed measurements systems with polytopic-type parameter uncertainties and disturbances. The objective is to make the system output follow the output of a system model and to attain guaranteed H_∞ performance of the proposed adaptive control scheme. 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, model following performance and prescribed H_∞ disturbance attenuation level 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.