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

Relative/multiplicative error bounds in Wang and Safonov (1990,1992) for the BST algorithm are extended to nonsquare transfer matrices. The equivalence of the BST algorithm to the inversely balanced truncation is established. Model reduction with relative/multiplicative error bounds is applied to LQG controller reduction which leads to simultaneous reduction of the plant and controller. Robust stability conditions are derived for the use of reduced order LQG controller. Moreover robust stability and robust stabilization problems are solved for general coprime factor uncertain systems involving H_∞ bounded relative/multiplicative uncertainties. Finally performance of the standard unity feedback system is analyzed for reduced order LQG controller with quantitative a priori bounds