A state-space based design of generalized minimum variance controller equivalent to transfer-function based design

This paper proposes a new generalized minimum variance controller (GMVC) using state-space approach. The controller consists of a state feedback and a reduced-order observer with poles at z = 0. A coprime factorization of the state-space based controller is also obtained. It is shown that the GMVC designed by state-space approach is equivalent to the GMVC given by solving Diophantine equations and polynomial approach. The equivalence is proved by comparing coprime factorizations of the two controllers. From the results of this paper, it may be possible to apply advanced design schemes given by state-space control theory to the design of GMVC.