Nonlinear model‐predictive control: Closed‐loop stability analysis

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.