Generalized Chain-Scattering Approach to H ∞ Control Problems

This paper gives a unified framework of H ^∞ control problem based on the generalized chain-scattering representation of the plant. The chain-scattering representation which is particularly useful in dealing with the cascade feedback connection is generalized to deal with general H ^∞ control problems including the four-block case. It is shown that the stability of the closed-loop system is easily dealt with by chain-scattering representation, without recourse to Youla parameterization. The general four-block H ^∞ control problem is reduced to finding a J-lossless factorization of a chain scattering representation of the plant. This factorization which is a generalization of the celebrated inner-outer factorization in H ^∞ turned out to be the most fundamental notion of H ^∞ control theory.