On the asymptotically optimal tuning of robust controllers for systems in the CD-algebra: The case of sinusoidal reference signals

Recently the authors have shown that the general design ideas for robust controllers that are suitable for stable systems with step reference and disturbance signals are valid for more general classes of signals: in [1] for linear combinations of sinusoids and in [2] for linear combinations of sinusoids and polynomials and their products. The analysis in [1] is for parabolic systems in the time domain and in [2] for systems in CD-algebra in the frequency domain. The controller consists of a scalar gain ε and matrix gains K_k. The tuning problem is in finding optimal values for these gains. In this paper we investigate the tuning of the matrix gains of the controller as ε → 0. The cost function consists of H_∞-norm of the error between the reference signal and the measured output signal. Closed forms for asymptotically globally optimal solutions are given.