A graph theoretic approach to determining the transfer functions of mechanical networks, towards efficient computation of their $H_{2}$ norms

An alternative method for the determination of a transfer function of a single-input single-output mechanical system is given, illustrated with a model of a train suspension system taken from [5], and its application in
$H_{2}$
norm analysis following [7]. This example is demonstrated with a MATLAB workbook, which follows the example step-by-step, calculating the
$H_{2}$
norm from this transfer function numerically and symbolically. Building on this, this method is then embedded within an interior point optimisation scheme within MATLAB, demonstrating how a workflow using these methods may look, and demonstrating a speed up factor of around 20 times. Computation time is given and compared to existing methods built in to MATLAB. The associated code to reproduce all results in this paper can be found on Github [6].