Solutions to frequency weighted optimal H∞ model reduction problem

A frequency weighted optimal H_∞ model reduction problem for linear time-invariant (LTI) systems is considered. The objective of this class of model reduction problems is to minimize the H _∞ norm of the frequency weighted truncation error between a given LTI system and its lower order approximation. A necessary and sufficient solvability condition is derived in terms of LMIs with one extra coupling rank constraint, which generally leads to a non-convex feasibility problem. Moreover, it has been shown that the reduced-order model is stable when both stable input and output weights are included