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We propose a new convex linear parameter varying (LPV) controller design conditions that regionally stabilize LPV discrete-time systems under magnitude and rate saturating actuators. Moreover, the closed-loop system has an ensured exponential stability performance. The design conditions provide regional stabilization in the sense of polyquadratic stability, allowing an estimate of the region of initial conditions yielding trajectories with guaranteed convergence to the origin. A nonlinear first-order model models the magnitude and rate saturation of the actuators. Additionally, we propose a convex optimization procedure to enlarge the estimate of the region of attraction. Our approach is used in real-time nonlinear level control, illustrating the potentialities of the practical application of the method.

We propose convex conditions to synthesize parameter-dependent state feedback control gains to regionally stabilize discrete-time linear parameter varying (LPV) systems subject to magnitude and rate saturating actuators. The regional stabilization is performed in the sense of polyquadratic stability. Through a parameter-dependent Lyapunov function candidate, the design conditions are proposed in terms of a finite set of linear matrix inequalities (LMIs). The feasibility of the proposed conditions also provides an estimate of the region of initial conditions yielding trajectories with guaranteed convergence to the origin. We provide a design parameter to increase the contractivity of the Lyapunov function. Nonlinear first-order models represent the magnitude and rate saturation of the actuators. Additionally, we propose a convex optimization procedure to enlarge the estimate of the region of attraction. Three numerical examples illustrate our proposals' efficiency and compare the achieved results with other literature approaches.