Eigenvalue of Phi in state space must no be negative?

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.

--
Tim Wescott
Control systems and communications consulting
http://www.wescottdesign.com

Need to learn how to apply control theory in your embedded system?
"Applied Control Theory for Embedded Systems" by Tim Wescott
Elsevier/Newnes, http://www.wescottdesign.com/actfes/actfes.html

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.

--
Tim Wescott
Control systems and communications consulting
http://www.wescottdesign.com

Need to learn how to apply control theory in your embedded system?
"Applied Control Theory for Embedded Systems" by Tim Wescott
Elsevier/Newnes, http://www.wescottdesign.com/actfes/actfes.html