In this section, we discuss the state-feedback mixed /-control problem for discrete-time nonlinear systems. We begin with an affine discrete-time state-space model defined on in coordinates (x1,…,xn) :
where all the variables and system matrices have their previous meanings and dimensions respectively. We assume similarly that the system has a unique equilibrium at x = 0, and is such that f(0) = 0 and h10) = 0. For simplicity, we similarly also assume the following hold for the system matrices.
Assumption 11.2.1 The system matrices are such that