Model Reduction with Relative/Multiplicative Error Bounds and Relations to Controller Reduction

Model reduction with a priori relative/multiplicative error bounds in L 1 norm is studied. Inverse-weighted balanced truncation (IWBT) is proposed that is a variant of the Enns' algorithm 8]. It is shown that IWBT is equivalent to the balanced stochastic truncation (BST). This equivalence leads to the extension of an improved relative/multiplicative error bound for BST obtained by Wang and Safonov 35, 36] to general nonsquare transfer matrices. Natural relations between IWBT and observer-based controller reduction are investigated that motivates the simultaneous reduction of the plant and controller through coprime factor reduction. Robust stability conditions for simultaneous reduction of the plant and the controller are established for the closed-loop system consisting of full order plant and reduced order controller. As a byproduct, robust stability and stabilization problems are solved for general coprime factor plant descriptions with relative/multiplicative H 1 bounded uncertainties. Similar results are obtained for coprime factors of the feedback controller involving relative/multiplicative H 1 bounded uncertainties. These results resemble those for gap metric uncertain systems while hold true for general coprime factor uncertain systems. Moreover performance degradation of the feedback system using reduced order controller is analyzed with quantitative a priori bounds.