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We prove a necessary and sufficient condition for the exponential  stability of time-invariant linear systems on time scales in terms of  the eigenvalues of the system matrix. In particular, this unifies the  corresponding characterizations for finite-dimensional differential  and difference equations. To this end we use a representation formula  for the transition matrix of Jordan reducible systems in the  regressive case. Also we give conditions under which the obtained  characterizations can be exactly calculated and explicitly calculate  the region of stability for several examples.

A spectral characterization of exponential stability for linear time-invariant systems on time scales