Introduction

Many properties of the linear system Ld will recur repeatedly and Chapters 5 and 6 survey some of those most commonly used. Several advantages accrue to this concentrated exposition. The various controllability and observability properties have a propensity for arising as technical conditions in a host of later policy analyses. Their explication now, prior to their use, avoids the inevitable digression their subsequent introduction will otherwise entail. But, just as importantly, their juxtaposition in these chapters emphasises similarities and differences, as well as basic theoretical significances, which are likely to go unremarked if these properties are introduced across later chapters when technical needs dictate.

There has been in the relevant economics literature a tendency to treat these various controllability and observability properties as technical conditions only, devoid of any intuitive significance. This is probably characteristic of initial interdisciplinary applications, but also partially reflects the representational differentiation of the linear system discussed in Section 4.4. This differentiation, by inhibiting access to the linear systems literature, has also inhibited the development of the conceptual significance of technical properties like controllability and observability. The primary motivation for Chapters 5 and 6 is accordingly expositional, and the work of system theorists such as Kalman, Ho and Narendra (1963), Desoer (1970), Wonham (1967), Hautus (1969,1970), and Zadeh and Desoer (1963) is employed extensively.

Chapter 5 concerns itself with the fundamental property of state controllability, and does so along three fronts.