Controller reduction with closed loop performance guarantee

This paper describes a modification of a singular value decomposition (SVD) based controller reduction method recently proposed in [13]. Instead of formulating a ℋ₂ norm characterizing generalized controllability Gramian inequality as in the previous case, the current method applies the bounded-real lemma to certify the closed loop performances in ℋ_∞ norm. In addition, unlike the previous method, the current one does not suffer from the lack of symmetry that all the data from the plant is not utilized. Yet, the current method inherits the same merit as the previous one that the formulated problem can be solved as a generalized minimum rank matrix approximation problem which can be solved efficiently using SVD. Extensions and numerical examples are shown in the end.