Balanced performance preserving controller reduction

Performance preserving controller reduction via additive perturbation of the closed-loop transfer function

“…First, solve kW 01 2 (G0G r )W 01 1 k 1 reduction directly to obtain Kr. Methods to solve kW 01 2 (G 0 Gr)W 01 1 k1 reduction directly are given in [12]. Second, using (4) and(5), approximate kW 01 2 (G 0 Gr)W 01 1 k1 reduction by kW 01 2 V 2 (K 0 K r )V 1 W 01 1 k 1 reduction and then use frequency weighted model reduction methods to obtain…”

“…Instead of using additive perturbation on the controller, proposed by Goddard and Glover, our method is based on additive perturbation on the closed-loop transfer function. Compared with Goddard and Glover's method, our method has two advantages: first the orders of the proposed weightings in our method are much lower; second our method can be used with many existing controller reduction methods [7], [9], [12] since there is a close relationship between our method and the existing methods.…”

Weighted Model Reduction via Interpolation

“…The weighted model reduction problem is tackled most often using variants of frequency-weighted balanced truncation; see Varga and Anderson [2003], Anderson and Liu [2002], Schelfhout and De Moor [2002], Gugercin and Antoulas [2004], Enns [1984], Wang et al [2002], Lin and Chiu [1992], Wang et al [1999], Sreeram and Ghafoor [2005] and references therein. For approaches that seek to minimize a weighted-H 2 error, see Halevi [1992] and Spanos et al [1992].…”

Generalised gramian framework for model/controller order reduction of switched systems

“…cheaper, simpler and more easily available hardware), ( ‡ ‡ ‡) relative computational efficiency and (iv) decreased effects of computational delay on closed-loop stability and performance. For these reasons, controller order reduction has received considerable attention in recent years (Anderson and Liu 1989;Zhou, De Souza, and Cloutier 1995;Zhou, Doyle, and Glover 1996;Wang, Screeram and, Liu 2002).…”