Robust simplified adaptive model following for linear time-delay systems

An output-feedback model-following problem is solved, for linear time-delay systems with uncertainties, using robust simplified adaptive controllers. Sufficient conditions for closed-loop stability of the proposed simplified adaptive control scheme are given, in terms of Bilinear Matrix Inequalities. Stability is analyzed using the Lyapunov-Krasovskii functional method. The solutions are delay-dependent; however, delay-independent results can be obtained, as a particular case, for certain values of the design parameters. A numerical example is given, which demonstrates the proposed method and the simplicity of its implementation.