Computation of minimum-time feedback control laws for discrete-time systems with state-control constraints

The problem of finding a feedback law that drives the state of a linear discrete-time system to the origin in minimum-time subject to state-control constraints is considered. Algorithms are given to obtain facial descriptions of the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</tex> -step admissible sets. These descriptions are then used to characterize the complete class of minimum-time feedback laws. Moreover, the characterization leads to a conceptually simple on-line implementation. The main ideas are illustrated with two simple examples.