H2-optimal model approximation by input/output-delay structured reduced order models

In this paper, the H2-optimal approximation of a multi-input multi-output transfer function by a finite dimensional system including input/output delays, is addressed. This problem is of particular interest when the full order model represents a transport phenomenon. The contribution is twofold : firstly, based on the pole/residue decomposition, an H2-inner product formula in the presence of input/output delays is derived. Secondly, the underlying H2 optimality conditions of the approximation problem are obtained as an extension of the tangential interpolatory conditions. It is also demonstrated that for fixed delay values, this problem can be recast as a rational function approximation one. An iterative algorithm is sketched out and numerical results assess the theoretical contributions.