Discrete Linear Time-invariant (LTI) Systems
For a discrete-time linear state-space system (i.e. time variable ) the state equation is
Where is an matrix and is a matrix (i.e. is inputs collected in a vector. The test for controllability is that the matrix
has full row rank (i.e., ). That is, if the system is controllable, will have columns that are linearly independent; if columns of are linearly independent, each of the states is reachable giving the system proper inputs through the variable .
Read more about this topic: Controllability
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