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:
“I can never get people to understand that poetry is the expression of excited passion, and that there is no such thing as a life of passion any more than a continuous earthquake, or an eternal fever. Besides, who would ever shave themselves in such a state?”
—George Gordon Noel Byron (1788–1824)
“The only people who treasure systems are those whom the whole truth evades, who want to catch it by the tail. A system is just like truth’s tail, but the truth is like a lizard. It will leave the tail in your hand and escape; it knows that it will soon grow another tail.”
—Ivan Sergeevich Turgenev (1818–1883)