Nonlinear scheduled control for linear systems subject to saturation with application to anti-windup control

In this paper we propose a nonlinear state-feedback control law for the global asymptotic stabilization (GAS) of non-exponentially unstable plants. For these types of plants, nonlinear controllers are necessary in general to achieve GAS and several results are available in the literature. The theory is then also used as a solution to the so-called anti-windup problem for these types of plants. The advantages of the approach here proposed, in addition to a formal stability proof, are that it is not computationally intensive, therefore prone for real-time implementation on plants with fast dynamics and that it induces fast transients and converges to the desired equilibrium in set-point regulation. Various examples illustrate the effectiveness of the proposed control laws both in the stabilization and in the anti-windup design task.