Hankel norm computation for linear time-invariant systems with multiple feedthrough delays

We are concerned with the computation of the Hankel norm for stable linear time-invariant systems with multiple input delays. Firstly, the boundedness and compactness of the Hankel operator are examined. Next, the norm computation problem is transformed into an optimization problem. Then the variational principle is used to find its solution, which leads to solving differential equations. After change of variables, we convert these equations into a set of differential-algebraic equations defined on the closed interval with length equal to unit delay time. Our result shows that the value of the Hankel norm is just the largest root of one algebraic equation which actually is the determinate of a certain complicated matrix including the effect of length of delay time and total number of delays in the dynamical systems