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:

    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)

    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)