Talk:Control Systems/Linear System Solutions

Regarding the use of spectral decomposition to compute the state transition matrix $$e^{\mathbf{A}t}$$ there's a point which I think is unclear. If a vector $$\vec{v}$$ is an eigenvector of the matrix $$\mathbf{A}$$, then another vector $$k\vec{v}$$ is also an eigenvector, for a scalar constant $$k$$. Putting this into the spectral decomposition equation, we find that the constant comes to the front of that term of the summation.

I suspect that there's supposed to be a relationship between the right and left eigenvectors in such a way that the constant will be cancelled out when they are multiplied, but I can't seem to find a reference that defines exactly what the relationship is. I think that the matrix of left eigenvectors should be the inverse of the matrix of right eigenvectors, but someone more qualified should check this before it goes into the actual book.

statetrans function
I don't believe the matlab function given to calculate the state transition matrix gives correct values. I don't believe that this should be included in the section. Also when taking e^A where A is a matrix in matlab it is best to use the expm function and not exp--Esj88 (discuss • contribs) 04:43, 5 January 2012 (UTC)