A Smith Factorization Approach to Robust Minimum Variance Control of Nonsquare LTI MIMO Systems

The minimum phase systems have ultimately been redefined for LTI discrete-time systems, at first SISO and later square MIMO ones, as those systems for which minimum variance control (MVC) is asymptotically stable, or in other words those systems who have ‘stable’ zeros, or at last as ‘stably invertible’ systems. The redefinition has soon been extended to nonsquare discrete-time LTI MIMO systems (Latawiec, 1998; Latawiec et al., 2000) and finally to nonsquare continuous-time systems (Hunek, 2003; Latawiec & Hunek, 2002), giving rise to defining of new ‘multivariable’ zeros, i.e. the so-called control zeros. Control zeros are an intriguing extension of transmission zeros for nonsquare LTI MIMO systems. Like for SISO and square MIMO systems, control zeros are related to the stabilizing potential of MVC, and, in the input-output modeling framework considered, are generated by (poles of) a generalized inverse of the ‘numerator’ polynomial matrix (.) B . Originally,