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this video provides some hand-worked examples for students to go through its been shown that there are two simple controllability tests for states based models and the tests are the same whether you have a continuous state space model or a discrete state space model and here weve emphasized that were going to have n States so the controllability matrix must be full rank and the controllability matrix is defined as M C equals B comma a B all the way up to a to the N minus 1 B alternatively you can check the matrix VB must have no zero rows where V is that left eigenvector so W lambda V is the eigen value eigen vector decomposition of the matrix a in practice an eigen value eigen vector decomposition is non-trivial and not a paper and pen exercise you would have to do that by computer and so these examples were going to focus on the use of the controllability matrix which is given here now even though this is a bit more straightforward it is reiterated that in the vast majority of c
