Representation, Approximation, and Identification

This chapter describes mathematical representation, approximation, and identification of, in most cases, nonlinear systems. An ideal representation of a real system is generally impossible, so that system approximation becomes necessary in practice. Intuitively, approximation is always possible. However, the key issues are what kind of approximation is good, where the sense of "goodness" must first be defined, of course, and how to find such a good approximation. The fundamental issue in representing a physical system by a mathematical formulation, called a mathematical model, is its correct symbolization, accurate quantization, and strong ability to illustrate and reproduce important properties of the original system. A higher level mathematical model is needed to provide a qualitative and quantitative representation of the real physical circuit. Mathematical modeling via differential equations and via state-space descriptions are the most basic mathematical representation methods.