Inequalities between L-2 and L-infinity norms of strictly proper stable transfer functions

In this paper we shall derive two inequalities between the L2 and L?? norms of stable transfer functions defined by H(s) = C(sI - A)-1B and show that ||H||F ?? ??2Tr(-A)||H||?? and for a single input or single output transfer function ||H||2 ?? 1.172(d1 2 + 2d2)1/4 ||H||?? where det(sI - A) = sn + d1sn-1 + d2sn-2 + ...