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- Is system stable if poles lie on unit circle?
- Is system stable if poles on imaginary axis?
- What is stability discuss the effect of location of poles on the stability?
- What is the significance of unit circle for stability analysis in z domain?
Is system stable if poles lie on unit circle?
Poles of Discrete-Time Transfer Function
For stable discrete systems, all their poles must have a magnitude strictly smaller than one, that is they must all lie inside the unit circle. The poles in this example are a pair of complex conjugates, and lie inside the unit circle. Hence, the system sys is stable.
Is system stable if poles on imaginary axis?
If the system has two or more poles in the same location on the imaginary axis, then the system is unstable. If the system has one or more non-repeated poles on the imaginary axis, then the system is marginally stable.
What is stability discuss the effect of location of poles on the stability?
Poles and Stability
When the poles of the closed-loop transfer function of a given system are located in the right-half of the S-plane (RHP), the system becomes unstable. When the poles of the system are located in the left-half plane (LHP) and the system is not improper, the system is shown to be stable.
What is the significance of unit circle for stability analysis in z domain?
The Unit Circle at the Z-plane is the set of points z to which the Z-Transform equals the Discrete Time Fourier Transform (DTFT) and also, if you map it to the s-Plane, it corresponds to the Imaginary axis. A Causal system is stable if all poles are inside the unit circle.
