- a system is controllable iff there is an input u(t) that will cause the system to go from any initial state to any final state in a finite time.

- stabilizable if it is controllable or if the uncontrollable nodes are stable.

- If an input is to be observable it must be detectable in the output. For example consider the following state equations.


• This can be verified with the


• Another test for controllability is,


• Yet another test for controllability is,


• For a system to be controllable, all of the states must be controllable.

• If a system in uncontrollable, it is possible to make it observable by changing the model.

• A pole-zero cancellation is often the cause of the loss of observability.

• if all unstable modes are controllable, the systems is said to be stabilizable.

• The principle of Duality requires that a system be completely observable to be controllable.

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