Unified approach to h^∞-optimization, hankel approximation and balanced realization problems

A unified approach is proposed here to solve three problems simultaneously, namely Hm-optimization, Hankel approximation and minimal balanced realization for scalar systems. It is shown that all these problems can be reduced to the same standard form wherein merely the singular-value decomposition (SVD) of an easily constructed square matrix is required to establish the final solutions. The formulation is solely in terms of the coefficients of a transfer function and the resulting algorithm can be performed in a very computationally efficient way.