A J-lossless factorisation approach to H∞ control in delta domain

The paper addresses problems of numerical conditioning of a chain-scattering approach based on a J - lossless coprirne factorisation to the discrete-time H_∞ - control. It is demonstrated that common forward shift operator techniques may become ill-conditioned for a sufficiently small sampling period and that numerical robustness can be significantly improved via utilising the so-called delta operator formulations of the origin problem. Solutions are obtained via solving two coupled delta-domain Riccati equations leading to J-lossless coprirne factorisations of a chain scattering description of a controlled plant. In order to evaluate a measure of numerical conditioning of these solutions a relative condition number of the delta-domain algebraic Riccati equation is introduced.