Introduction to Mathematical Systems Theory pp 151-199 | Cite as

# 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 }.

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