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

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