Convolution and Hankel operator norms for linear systems

Some novel operator norms for the convolution and Hankel operators of time-invariant, linear systems are introduced. Using these norms, new controller design problems arise which will require modifications to the previous H² approach, where a trace operator was used in the performance index. The results suggest that the λ_max and d_max operators are more appropriate if the intention is actually to limit the amplitude variations of the controlled variables rather than minimize mean square error