Smoothed spectral abscissa tuning of an observer-predictor for input delay compensation of distributed time-delay systems

This manuscript presents an observer-based control for the compensation of the input delay in linear systems including pointwise and distributed delays, for which the smoothed spectral abscissa plays an important role in the tuning task. Specifically, tuning the state feedback gains of the observer-based control by optimizing the smoothed spectral abscissa, minimizes the
$\mathcal{H}_{2}$
norm of the corresponding closed-loop system. Furthermore, tuning the observer gains by optimizing the smoothed spectral abscissa of the dynamic observer errors, ensures a fast convergence of the observer-based control to the future state. The proposed controller is applied to the stabilization of combustion in a rocket motor chamber.