Modelling a Broad Class of Actuator Saturations Using Takagi-Sugeno Models with a Reduced Number of Local Models

In this paper, the Takagi-Sugeno (T-S) models are suggested as modelling tools to represent both the behavior of a nonlinear system and its saturated actuators. Given a T-S system with
$r$
local models, previous works on input saturation usually required
$2^{n_{u}}r$
or
$3^{n_{u}}r$
local models to represent an actuator saturated outside of an orthotope
$(n_{u}$
stands for the input vector dimension). In this paper, an elementary representation is suggested, which only takes
$2r$
local models (thus, independently of
$n_{u}$
), and is able to capture a much broader class of actuator saturations. Local stabilization conditions expressed as linear matrix inequalities (LMI) are provided using the conventional static parallel distributed compensation (PDC) state feedback scheme. A heuristic solution is given in order to ensure a large guaranteed domain of attraction. Numerical examples are given in order to demonstrate the proposed approach and initiate a discussion on its contributions and limitations.