Improved results on H8734; model reduction for continuous-time linear systems over finite frequency ranges

This paper revisits the H ∞ model reduction problem for continuous-time linear systems over finite frequency ranges. Given an asymptotically stable system, our goal is to find a stable reduced-order system in such a way that the error of the transfer functions between the original system and the reduced-order one is bounded over a finite frequency range. By virtue of the generalized Kalman-Yakubovich-Popov (GKYP) Lemma, we first establish necessary and sufficient characterizations for this problem in terms of linear matrix inequalities (LMIs). For the low- and mid-frequency cases, through introducing a non-conservative multiplier and resorting to the projection lemma, the reduced-order system matrices are decoupled with the matrix variables from the GKYP Lemma. Then, by introducing a new diagonal matrix variable and based on congruence transformation, the reduced-order system matrices are further decoupled with the matrix variable induced by the projection lemma and can be parameterized by a new matrix variable. The results are extended to the high-frequency case without the use of projection lemma to reduce the conservatism. Moreover, an iterative convex optimization algorithm is developed to solve the conditions. Finally, we demonstrate via numerical examples that our method can achieve much smaller approximation error than existing results.