Multiband H∞ control in a behavioural setting

The most appropriate mathematical background for the treatment of frequency domain specifications appears to be the H_∞ optimization theory. In this paper, a solution in the full information case of standard H_∞ control is given in a behavioural setting. It turns out that a good approximation to the optimal solution can be obtained by separate optimization in several frequency bands. Such a separation simplifies the procedure and sometimes reduces it to a primitive graphical technique. More importantly, the direct solution allows the designer to analyze the relationship between different frequency bands in the system. There are only a few basic constraints that need to be satisfied in order to tie together solutions in neighbouring frequency regions. Finally, an exact approach for estimating the accuracy of bandwidth truncation is developed on the basis of quadratic constraints