Pole-free GMVC and LQR designs for nonsquare LTI MIMO systems

Abstract

This paper presents (structurally stable) pole-free control designs for (a deterministic version of) generalized minimum variance control and linear quadratic regulation for nonsquare LTI MIMO systems. For both discrete-time control strategies, two alternative approaches are offered, the numerical one related with limiting control solutions as control weighting matrices tend to the zero ones and the other produced by analytically-derived perfect controls, for which it is possible to put the weighting matrices directly to the zero ones. In the latter case, the solutions are identical with that for minimum variance control, in which case the pole-free designs must account for the so-called control zeros, being the extension of transmission zeros for nonsquare LTI MIMO systems. Simulation examples illustrate the theoretical achievements of the paper.