Selection of a single uniquely specifiable [formula omitted] controller in the chain-scattering framework

Abstract

This paper studies the notion of central H ∞ controllers in the chain-scattering framework. Since in the chain-scattering framework the H ∞ control problem is equivalent to a factorisation problem that yields non-unique factors, it is important to somehow pin down these factors so that the resulting central controller is uniquely defined and corresponds to the central and minimum-entropy controller frequently discussed in the literature. In so doing, we devise a procedure for the selection of a single uniquely specifiable H ∞ controller in the chain-scattering framework. The chain-scattering framework is important because it has a distinct advantage over state-space based methods for some applications in that it poses and solves the H ∞ control problem entirely in an operator-theoretic setting, thereby allowing us to contemplate direct changes of the frequency domain symbols rather than changes in the corresponding state-space matrices.