On asymptotic behavior of non-square linear optimal regulators

This paper, considers the behavior of the finite optimal closed-loop poles for non-square multivariable systems. It is shown that, if the system is nonsquare, then some of the optimal closed loop poles asymptotically approach the location of (minimum phase) transmission zeros (or reflections of the non-minimum phase ones), some approach infinity, and yet others approach new locations, unrelated to the transmission zeros. These locations are referred to as "compromise zeros" A numerically stable technique is used to solve for the compromise zeros. The paper also investigates the behavior of optimal regulators in which the weighting matrices are chosen via the implicit model-following technique.