Eigenvalue of Phi in state space must no be negative?

According to Anstrom's "Computer controlled system" page 37 paragraph above example 2.5, in order there is a corresponding continuous
system, the eigenvalue of the state space matrix phi must not have eigenvalues on the negative real axis, why?
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On Tue, 25 Dec 2007 08:31:00 -0800, leaf wrote:

Eigenvalues on the negative real axis in the sampled time domain correspond to continuous-time eigenvalues with infinite real parts. That's kind of hard to achieve in practice.
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Tim Wescott
Control systems and communications consulting
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On Tue, 25 Dec 2007 15:24:54 -0600, Tim Wescott wrote:

I should also mention that there is an uncertainty in the mapping of eigenvalues back from the z domain to the s domain. The magnitude of the z-domain eigenvalue maps unambiguously to the s domain, but the polar angle of the eigenvalue in the z domain maps to an infinite number of eigenvalues spaced at 2 * pi * sampling frequency apart in the imaginary direction in the s domain.
So you can take a system description in the z domain and come up with _a_ continuous-time system, maybe, but you can't come up with _the_ continuous-time system without some further constraints on the eigenvalues.
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Tim Wescott
Control systems and communications consulting
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