A new approach to the LQ design from the viewpoint of the inverse regulator problem

A new design method of LQ regulators is developed by reverse application of pertinent results on the inverse regulator problem. The LQ regulator of interest here is, unlike the usual one, designed without specifying a quadratic cost, but it proves to minimize some quadratic cost; hence, it possesses those well-known robustness properties shared by all LQ regulators. A basic design procedure is developed first, and followed by practical ones in which the design parameters are chosen based on asymptotic modal properties of the regulator. This new method requires no Riccati solutions, thereby leading to simplification of the LQ design as compared to the usual one.