Controllability

Two properties of the linear state space system descriptions that are often needed in proofs about existence of certain types of controllers and state estimators are controllability and observability. Although these have important and easily visualized interpretations in terms of the natural language definitions of the words, it should be recognized that they are ultimately technical terms, used as shorthand to summarize properties of the system that allow certain types of controllers and state estimators to be designed. In particular, a system that is not controllable is not ‘uncontrollable’ in the natural language sense, nor is a not observable system ‘unobservable’.