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A characterization of eAtand a constructive proof of the controllability criterion

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1 Author(s)
Vidyasagar, M. ; Sir George Williams University, Montreal, P. Q., Canada

A differential equation characterizing the functions \alpha _{i}(t) , which arise when eAtis expressed as \alpha _{0}(t)I + ... + \alpha _{n-1}(t) A^{n-1} , is derived. It is shown that the set of functions {\alpha _{i}(t)} is linearly independent over any nonzero interval. Using this fact, a constructive proof is given for the well-known criterion for a linear time-invariant system to be controllable, namely, rank [B|AB| ... |A^{n-1}B] = n .

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Automatic Control, IEEE Transactions on  (Volume:16 ,  Issue: 4 )