Introduction to Dynamic Systems

This chapter is a brief summary of the main topics in dynamic system analysis and control, which are employed in this book. The chapter is also preliminary to the brief introduction of the embedded model control methodology outlined in Chapter 14 . Dynamic systems are described in terms of continuous-time and discrete-time (DT) state equations. Transfer functions and matrices, especially their low-frequency and high-frequency asymptotes, are derived for linear time invariant systems. The main properties of dynamic systems are recalled, namely stability, controllability, and observability. The core of the chapter is the derivation of the prediction error and tracking error equations together with their transfer function relations, as they are employed by the performance and stability inequalities throughout the book. The last part of the chapter focuses on DT random processes (continuous time processes are also mentioned), as they are the ingredients of the disturbance dynamics. The chapter ends with a brief outline of the hybrid and DT Kalman filters.