Gain-Scheduling Control Synthesis with Inescapability Conditions for Nonlinear Systems Under Input Saturation

This paper proposes a novel methodology to design a gain-scheduled state-feedback control law for nonlinear systems subjected to input saturation constraints and bounded external disturbances. The overall goal is disturbance rejection understood as determining the smallest possible inescapable set starting from zero initial conditions. The control design is addressed via iterative algorithms based on Linear Matrix Inequalities, which are obtained from the application of
$\mathscr{H}_{1}$
star norm together with small gain argumentations. Numerical simulations are provided to show the effectiveness of the proposed method.