In this article, the stabilization problem of discrete-time bilinear systems by state-feedback control is investigated. First, necessary and sufficient conditions guaranteeing positive invariance or/and attractivity of polyhedral sets of general form with respect to quadratic systems are provided. These results are then used to establish systematic methods of determining linear and nonlinear state feedback control laws making a prespecified polyhedral set a domain of attraction with respect to the resulting closed-loop system, even in the presence of input constraints.
|Title of host publication||Proceedings of the 18th IFAC World Congress, August 28-September 2, 2011, Milan, Italy|
|Publication status||Published - 2011|