Regional stabilization of rational discrete-time systems with magnitude control constraints

This work addresses the problem of local stabilization of rational systems considering magnitude control constraints. Based on a Recursive Algebraic Representation (RAR) of the system and on a generalized sector condition, stabilizing conditions in the form of linear matrix inequalities (LMIs) are proposed to compute a saturating state feedback control law that ensures the local asymptotic stability in a certain region of the state space. In this sense, a convex optimization problem is proposed to determine a control law aiming at maximizing an estimate of the region of attraction of the closed-loop system. An extension of the method to consider a quadratic performance criterion is also presented.