ABSTRACT
In this chapter we will introduce the basic building blocks necessary to understand linear time-invariant, multivariable systems.Wewill examine solutions of linear systems in both the time domain and frequency domain. An important issue is our ability to change the system’s response by applying different inputs.We will thus introduce the concept of controllability. Similarly, we will introduce the concept of observability to quantify how well we can determine what is happening internally in our model when we can observe only the outputs of the system. An important issue in controllability and observability is the role of zeros. We will define them for multivariable systems and show their role in these concepts. Throughout, we will introduce the linear algebra tools necessary for multivariable systems.
