On Computing 2-Norms of Transfer Function Matrices

In this paper, efficient algorithms are proposed for computing L² and L² norms of the transfer function matrices of continuous and discrete systems, respectively. The algorithms are general, they are applicable for both stable and unstable systems. For unstable systems, new algorithms are proposed which include as a first main step, the computation of a suitable left coprime factorization of the given transfer function matrix. The algorithms are oriented toward efficient computer implementations using available, high quality numerical software.