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

A polynomial approach is pursued for locally stabilizing discrete-time linear systems subject to input constraints. Using the Youla-Kucera 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 semidefinite programming. Key topics are touched on the stabilization of MIMO plants or maximization of the size of the stability domain. Readily implementable algorithms are described.