Controllability and Observability

Abstract

In this chapter we introduce two concepts that play a central role in systems theory. The first concept is controllability; the second is observability. Loosely speaking, we call a behavior controllable if it is possible to switch from one trajectory to the other within the behavior. The advantage is that in a controllable behavior, one can, in principle, always move from an”undesirable” trajectory to a “desirable” one. Observability, on the other hand, is not a property of the behavior as such; rather it is a property related to the partition of the trajectories w into two components w ₁ and w ₂ . We call w ₂ observable from w ₁ if w ₁ and the laws that governing the system dynamics uniquely determine w ₂ . Thus observability implies that all the information about w is already contained in w ₁ .