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