I. Introduction
Input saturation is a common feature in applications of control systems technology and it might severely affect system operation if not properly addressed. With regards to linear time-invariant (LTI) systems, a rich literature has been built over the last decades, where the problem of saturated linear state feedback design was tackled under different perspectives [1]. In [2], for example, a local sector condition was applied for controller design using a simple relationship between a linear feedback and a dead-zone nonlinearity. Alternatively, another popular strategy is based on a convex hull representation of the saturated control and is known as the polytopic approach [3]. The notion that a contractively invariant ellipsoid can be used for estimating the closed-loop domain of attraction is common to both strategies, as quadratic Lyapunov functions are a standard tool for stability analysis of linear systems. In general, it has been claimed based on computations that the polytopic framework provides larger invariant ellipsoids than sector-based conditions, at the expense of a higher computational cost [1]. The same arguments have been put forward over the problem of anti-windup design, which aims at reducing the negative impact of saturation upon a feedback system that is already held stable by a suitable dynamic output feedback [4]–[6].