This paper proposes a new design framework of control systems based on chain-scattering representation of the plant. The chain-scattering representation has several advantages over the conventional input-output description of the plant. It can represent the feedback connection in a simple way, which makes the role of factorization explicitly clear. It has a strong symmetry (duality) to its inverse. It clarifies the meaning of pole-zero cancellation. In this paper, we shall exploit some algebraic properties of the chain-scattering representation of the plant which are relevant to control system design, especially to H ∞ control.
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