Generalised minimum variance control state-space design

The main goal of this study is to propose a state-space design technique for the generalised minimum variance control. In this sense, the same results achieved in the transfer function design framework are granted by the state-space method. It simplifies the design procedure while avoiding the solution of the Diophantine equation. Instead, the minimum variance predictor is obtained by the direct feed-through of an estimated state vector using a Kalman filter designed directly from the state-space model and without the need to solve an algebraic Riccati difference equation. In this way, even when dealing with systems with long time delays, the design procedure requires only a small amount of work as compared to the classical Diophantine-dependent technique. The proof of equality between the transfer function and state-space methods is easily verified by simple linear algebra, showing that the Diophantine equation results are intrinsically embedded in the gains of the state-space predictor derived, which means that resultant polynomials of the Diophantine equation can also be obtained by construction with the new design method. Two simulation examples are given to demonstrate the proposed technique.