Synthesis of polynomial static state feedback laws and analysis for discrete-time polynomial systems with saturating inputs

In this paper we provide conditions for the synthesis of polynomial static state feedback control laws for discrete-time polynomial systems and conditions for the stability analysis of input-saturating systems. These conditions are based on polynomial inequalities affine both in the Lyapunov function parameters and in the gains of the polynomial state-feedback control law. The stability analysis of the saturating system is performed with polynomial Lyapunov functions with the help of a generalized sector condition which allows us to take into account nonsymmetric saturation bounds. The problems of computing the polynomial control laws and estimating the region of attraction of the resulting closed-loop system are solved numerically by considering sum-of-squares relaxations of the polynomial inequalities.