On approximate model-reference control of SISO discrete-time nonlinear systems

For discrete-time single-input single-output nonlinear plant and reference model, the model matching problem does not have an exact solution if the relative degree of the plant is larger than that of the reference model, but only approximate solutions can be considered. The notion of best approximate controller strictly depends on the definition of distance between the control system and the reference model. The goal of the paper is to analyze the performance limitations, which are inherently present because of the mismatch between the relative degrees of the plant and the model. Two different types of reference models (linear and nonlinear), and two different notions of distance (8-norm-based and 2-norm-based distance) are considered. Upper and lower bounds for the maximum achievable performances are given, as a function of the parameters of the reference model.