Robust simple adaptive model following for linear time-delay systems with guaranteed H_∞ performance

An output-feedback model-following problem is solved for linear time-varying delay systems with polytopic type parameter uncertainties and disturbances, using a simple direct adaptive control scheme with an additional proportional gain term, which is applied to the tracking error. The objective is to obtain sufficient conditions for closed-loop stability and guaranteed H∞ performance of the proposed adaptive control scheme, so that the system output follows the output of the model. Sufficient conditions for closed-loop stability, model-following performance and prescribed H∞ disturbance attenuation level of the proposed simple adaptive control scheme are given in terms of bilinear matrix inequalities. Stability is analysed using the Lyapunov-Krasovskii functional method, and both delay-dependent and delay-independent results are obtained. The proposed controller does not utilize the knowledge of the delay; only the bounds on the delay and the delay rate are used. Numerical examples are given, which demonstrate the effectiveness of the proposed controller and the simplicity of its implementation.