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
Famous quotes containing the words continuous and/or systems:
“We read poetry because the poets, like ourselves, have been haunted by the inescapable tyranny of time and death; have suffered the pain of loss, and the more wearing, continuous pain of frustration and failure; and have had moods of unlooked-for release and peace. They have known and watched in themselves and others.”
—Elizabeth Drew (1887–1965)
“What avails it that you are a Christian, if you are not purer than the heathen, if you deny yourself no more, if you are not more religious? I know of many systems of religion esteemed heathenish whose precepts fill the reader with shame, and provoke him to new endeavors, though it be to the performance of rites merely.”
—Henry David Thoreau (1817–1862)