Position of poles and Stability in $z$ domain

1. What is the condition for stability in Z domain?
2. How do you check stability using Z-transform?
3. How pole position affects the stability of the system?
4. When the system has poles inside the unit circle in Z domain?
5. What are poles in Z-transform?
6. Which region signifies the stable region in Z-plane?

What is the condition for stability in Z domain?

Equation (3.7. 6) gives the condition of stability in Z domain. This condition requires that, unit circle must be present in the ROC of H(Z). Otherwise we cannot find H(Z) on unit circle at all.

How do you check stability using Z-transform?

First, we check whether the system is causal or not. If the system is Causal, then we go for its BIBO stability determination; where BIBO stability refers to the bounded input for bounded output condition. The above equation shows the condition for existence of Z-transform.

How pole position affects the stability of the system?

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.

When the system has poles inside the unit circle in Z domain?

Explanation: If all the poles of H(z) are inside an unit circle, then it follows the condition that |z|>r < 1, it means that the system is both causal and BIBO stable.

What are poles in Z-transform?

The values of z for which H(z) = 0 are called the zeros of H(z), and the values of z for which H(z) is ¥ are referred to as the poles of H(z). In other words, the zeros are the roots of the numerator polynomial and the poles of H(z) for finite values of z are the roots of the denominator polynomial.

Which region signifies the stable region in Z-plane?

In simple words, the ROC is a region in the Z-plane consisting of all the values of Z which make the Z-transform (X(Z)) attain a finite value. The Region of Convergence is required to determine: the stability of a system by examining the transfer function. whether the system is causal or non-causal.