MODEL-REDUCTION WITH RELATIVE MULTIPLICATIVE ERROR-BOUNDS AND RELATIONS TO CONTROLLER REDUCTION/

Balanced model reduction with a priori relative/multiplicative error b ounds in L(infinity) norm is studied. Inverse-weighted balanced trunca tion (IWBT) is proposed that is a variant of the Enns' algorithm [3]. It is shown that IWBT is equivalent to the balanced stochastic truncat ion (BST). This equivalence leads to the extension of an improved rela tive/multiplicative error bound for BST obtained by Wang and Safonov [ 17], [18] to general nonsquare transfer matrices. Natural relations be tween IWBT and observer-based controller reduction are investigated wh ich motivate the simultaneous reduction of the plant and controller. R obust 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, robu st stability and stabilization problems are solved for general coprime factor plant descriptions with relative/multiplicative H-infinity nor m bounded uncertainties. Similar results are obtained for general copr ime factors of the feedback controller involving relative/multiplicati ve H-infinity norm bounded uncertainties. These results resemble those for gap metric as studied in [8], [14], and [19]. Moreover performanc e degradation of the feedback system using reduced-order controller is analyzed with quantitative a priori bounds.