20.3 CONTROLLABILITY

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- 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.