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:
“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)
“No civilization ... would ever have been possible without a framework of stability, to provide the wherein for the flux of change. Foremost among the stabilizing factors, more enduring than customs, manners and traditions, are the legal systems that regulate our life in the world and our daily affairs with each other.”
—Hannah Arendt (1906–1975)