A method to analyze the closed-loop stability of a system composed of a nonlinear process and a discrete controller is developed. The closed-loop system is described by a set of difference equations resulting from the discretization of the continuous-time model. A commonly used method of discretization (forward difference) offers an incorrect relative order compared to exact discretization. The state and input sensitivity equations of the continuous-time model are used in computing the nominal closed-loop stability criteria. The nominal stability analysis is extended to the important cases of unmeasured states and uncertain model parameters. A numerical Lyapunov function is used to estimate closed-loop regions of attraction. A simulation example (a CSTR with input multiplicity) presented illustrates the analysis methods and closed-loop behavior.