Model reduction with relative/multiplicative error bounds and relations to controller reduction

Balanced model reduction with a priori relative/multiplicative error bounds in L_∞ norm is studied. Inverse-weighted balanced truncation (IWBT) is proposed that is a variant of the Enns´ algorithm. 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 to general nonsquare transfer matrices. Natural relations between IWBT and observer-based controller reduction are investigated which motivate the simultaneous reduction of the plant and controller. 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 by-product, robust stability and stabilization problems are solved for general coprime factor plant descriptions with relative/multiplicative H_∞ norm bounded uncertainties. Similar results are obtained for general coprime factors of the feedback controller involving relative/multiplicative H_∞ norm bounded uncertainties