ABSTRACT
This chapter presents static models, starting with single-input single-output systems and moving first to multiple-input single-output then to multiple-input multiple-output systems. It discusses linear models and briefly reviews nonlinear structures and shows how their linear approximation can be obtained. The chapter addresses the input-output representation of linear discrete dynamic systems. It defines the poles and zeroes of the system. The chapter reviews the basic concepts of eigenvalues and eigenvectors, spectral decomposition and the Cayley-Hamilton theorem. It also reviews the modeling of continuous-time systems. The chapter also discusses the methods used to represent the input-output behavior of continuous-time linear time-invariant dynamic systems. It summarizes fundamental results of matrix algebra. The chapter describes the concepts of the rank of a matrix and the linear independence of vectors will be reviewed. It focuses on the physical systems we monitor and control are usually characterized by continuous-time operation.
