Controllability - Continuous Linear Systems

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)

    The skylines lit up at dead of night, the air- conditioning systems cooling empty hotels in the desert and artificial light in the middle of the day all have something both demented and admirable about them. The mindless luxury of a rich civilization, and yet of a civilization perhaps as scared to see the lights go out as was the hunter in his primitive night.
    Jean Baudrillard (b. 1929)