hello. in signal system and in the Z transformation, for stability it is must to |Z|
Your question is not well defined. If you have some difficulties to get the reason of that, I can share with you a nice lecture handout from a professor in my University. Unfortunately it is not that convenient to type the equations over here. The concept is explained very short and sweet but you're going to get it. I recommend you to refer to the page 23 of this handout. If you have any further question about the contents, I would be glad to help you.
@ Mohammad: Thank you for your time. I actually meant that the roots of Z must lie within the unit circle for that system to be stable. Just asked to have more understanding.
Then if you are so much interested in stability issues of the LTI systems I recommend you to study them for internal behavior of them because the BIBO stability is just a spacial and so called 'Input-output' stability case.
Strictly speaking, "stable" can be classified into "asymptotically stable" and "Lyapunov stable" (i.e., bounded response). Yeah, |z|
Yes, It is asymptotically stable. Mohammad Mahdi Momenzadeh It is a nice handout.
Yes, all the roots must lie within the unit circle.
The right way to write is |z|
Yes , a discrete time system is stable if and only if all the roots are located inside the unit circle |z|
- Badges
- Science topic
- Similar topics
- Engineering
- Control Theory
- Control Systems
- Control Systems Engineering