In this article, a primal-dual interior-point algorithm for semidefinite programming that can be used for analysing e.g. polytopic linear differential inclusions is tailored in order to be more computationally efficient. The key to the speedup is to allow for inexact search directions in the interior-point algorithm. These are obtained by aborting an iterative solver for computing the search directions prior to convergence. A convergence proof for the algorithm is given. Two different preconditioners for the iterative solver arc proposed. The speedup is in many cases more than an order of magnitude. Moreover, the proposed algorithm can be used to analyse much larger problems as compared to what is possible with off-the-shelf interior-point solvers.