Representations of linear time-invariant systems

Abstract

As already mentioned in Chapter 1, we adopt the approach in [64]—[68] in which a fundamental distinction is made between dynamical systems and their mathematical representations. In the next section we repeat the formal definition of a dynamical system as given by Willems [66]. In subsequent sections we consider various types of representations of dynamical systems. Polynomial matrices will play a fundamental role throughout the chapter. In fact, the study of behaviors in this book relies essentially on a module structure. Details are provided by the next section, which is tutorial and partly in the spirit of [7, Chapter 5]; we do not pretend the results to be new.