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:
“The habit of common and continuous speech is a symptom of mental deficiency. It proceeds from not knowing what is going on in other people’s minds.”
—Walter Bagehot (1826–1877)
“People stress the violence. That’s the smallest part of it. Football is brutal only from a distance. In the middle of it there’s a calm, a tranquility. The players accept pain. There’s a sense of order even at the end of a running play with bodies stewn everywhere. When the systems interlock, there’s a satisfaction to the game that can’t be duplicated. There’s a harmony.”
—Don Delillo (b. 1926)