Improved Gain-Scheduled Control Design for Rational Nonlinear Discrete-Time Systems with Input Saturation

An improved method of control design for rational nonlinear discrete-time systems with input saturation is proposed in this paper. Using Difference-Algebraic Representation (DAR) and parameter-dependent Lyapunov functions, a novel regional stabilization condition in terms of Linear Matrix Inequalities (LMI) is presented. Two optimization problems are addressed to either obtain the largest estimated Domain of Attraction (DoA) or minimize the
$\ell_{2}$
-gain from the energy-bounded disturbance input to the performance output. Numerical examples illustrate the potential of the proposed approach.