Control of linear systems subject to input constraints: a polynomial approach

A polynomial approach is pursued for locally stabilizing discrete-time linear systems subject to input constraints. Using the Youla-Ku cera parametrization and geometric properties of polyhedra and ellipsoids, the problem of simultaneously deriving a stabilizing controller and the corresponding stability region is cast into standard convex optimization problems solved by linear, second-order cone and semideenite programming. Key topics are touched on such as stabilization of MIMO plants or maximization of the size of the stability domain. Readily implementable algorithms are described. Their applicability is illustrated with several numerical examples.