On MIMO model reduction by the weighted equation–error approach

Abstract

The paper deals with the problem of approximating a stable continuous-time multivariable system by minimizing the L 2 -norm of a weighted equation error. Necessary and sufficient conditions of optimality are derived, and the main properties of the optimal reduced-order models are presented. Based on these conditions and properties, two efficient procedures for generating approximants that retain different numbers of Markov parameters and time moments are suggested and applied to benchmark examples. The results show that both the transient and the steady-state behaviour of the original systems are reproduced satisfactorily.

Routh--type $L_2$ model reduction revisited

“…Step 5, by particularising the polynomial identity (27). Finally, the transfer function of the approximating model has been determined according to Step 6; it turns out to bê G 3 (s) = 0.0724s 2 − 3.1780s + 5.8933 s 3 + 6.5248s 2 + 8.0224s + 5.8933 (34) whose poles are −5.2, −0.6624 ± 0.8334. In this case the squared L 2 error norm turns out to be 0.0662.…”

“…In this case the squared L 2 error norm turns out to be 0.0662. Figures 1, 2 and 3 compare, respectively, the impulse responses, the step responses and the Bode plots of (33) and (34) with those obtained using the method suggested in [11] and the balanced truncation method.…”