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A linear discrete-time system has t he characteristic equation, z3 – 0.81z = 0
The system
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- is stable
- is marginally stable
- is unstable
- stability cannot be assessed from the given information
Correct Option: A
Here linear discrete time system has characteristic equation
z3 – 0. 81 z = 0
⇒ z (z2 – 0.92) = 0
⇒ z (z – 0.9) (z + 0.9) = 0
Hence z = 0, 0.9, – 0.9
All roots lie inside unit circle. Hence the system is stable .
