State-space Representation and Analysis

The principles presented in Chapter 2 for studying fractional-order dynamic systems expressed in the input-output representation are extended in this chapter to the state-space representation. This chapter considers only systems that exhibit the following features, which are similar to those considered in the previous chapter: (1) systems are linear, (2) systems are time invariant, and (3) systems are of commensurate-order. We will show that this last property enables models and properties that are a quite straightforward generalization of well known results for integer-order LTI (linear time invariant) systems to be obtained. This chapter is divided into two parts: the first is devoted to the study of the representation and analysis of continuous systems, and the second studies discrete systems. Similar results are obtained for both kinds of systems in modeling, solution of the differential (or difference) equations, stability analysis, controllability, and observability.