An explicit parametric formula is obtained for time-optimal control of linear multivariable discrete-time systems by state feedback. This is achieved by introducing a so-called vector companion form and by examining the method of parametrization of this form. A careful study of the structural properties of these canonical forms leads to the definition of ‘regular’ and ‘irregular’ Kronecker invariants which facilitate the parametrization of the feedback controllers. In this paper, which is the first of two, the case of regular Kronecker invariants is formulated and an illustrative example presented.
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Karbassi et al. (1993) studied this question.
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