A note on balanced controller reduction

Controller reduction via stable factorization and balancing

“…Subsequently, various applications of balanced realizations were made to the controller reduction problem, e.g. Jonckheere and Silverman (1981), Verriest (198Ia, b), Yousuff and Skelton (1984), and Davis and Skelton (1985). Enns (1984) developed a frequency-weighted balanced realization technique for use in either model or controller reduction problems.…”

“…All these objections can in part be countered. First, one can design a high-order controller for the original system and then approximate the controller; see Yousuff and Skelton (1984). Second, one can additively decompose the system transfer function matrix into a stable and unstable part, and approximate just the stable part, and third, one can introduce appropriate frequency weighting into the approximation procedure, as in Enns (1984).…”

“…Yousuff and Skelton (1984) also suggest a rather ad hoc modification to cover the case of unstable controllers, and Davis and Skelton (1984) suggest a different modification which would deal with stable or unstable controllers (but without significantly more justification). A priori frequency domain bounds on the error associated with controller approximation are not known when the approximation procedure uses these modifications.…”

Reduced-Order LQG Controller Design by Minimizing Information Loss

“…The problem of controller reduction plays an important role in control theory and has attracted lots of attentions [1][2][3][4][5][6][7][8][9][10] in the fields of control theory and application. As noted by Anderson and Liu [2] , controller reduction could be done by either direct or indirect methods.…”

“…Examples of direct methods include optimal projection theory [3][4] and the parameter optimization approach [5] . Examples of indirect methods include LQG balanced realization [6][7][8] , stable factorization [9] and canonical interactions [10] . In the past, several model reduction methods based on the information theoretic measures were proposed, such as model reduction method based on minimal K-L information distance [11] , minimal information loss method(MIL) [12] and minimal information loss based on cross-Gramian matrix(CGMIL) [13] .…”