ABSTRACT
Control systems with actuator saturation are often encountered in practice. When actuator saturation occurs, in general global stability of an otherwise stable linear closed-loop system cannot be ensured. And the problem of estimating the domain of attraction for a system with a saturated linear feedback has been studied by many researchers in the last few years and various methods have appeared (see, [24, 140]). Model predictive control (MPC) is an effective control algorithm for dealing with actuator saturation. Many formulations have been developed for the stability of MPC (see, [18, 96]). Enlargement of the domain of attraction is achieved in [20, 28, 85, 90]. Anti-windup has been largely discussed and many constructive design algorithms have been formally proved to induce suitable stability properties (see, [25, 26, 27, 48, 68, 143]). Many of these constructive approaches rely on sector condition and S-procedure techniques and provide LMIs for the anti-windup compensator design. In some papers, notion of invariant set and LMI-based optimization approaches were proposed to estimate the stability regions by using quadratic Lyapunov functions and the Lur’e-type Lyapunov functions. In [17] and [142], the modeling of the nonlinear behavior of the system under saturation is made by using a polytopic differential inclusion and quadratic Lyapunov functions. For determining if a given ellipsoid is contractively invariant, [66] described a condition which is based on the circle criterion or the vertex analysis.
