Continuous Linear Systems
Consider the continuous linear time-variant system
There exists a control from state at time to state at time if and only if is in the column space of
where is the state-transition matrix.
In fact, if is a solution to then a control given by would make the desired transfer.
Note that the matrix defined as above has the following properties:
- is symmetric
- is positive semidefinite for
- satisfies the linear matrix differential equation
- satisfies the equation
Read more about this topic: Controllability
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