-1
$\begingroup$

What is the relation between causality and stability of a system??To be stable,is it must for the system to be also causal? and if the system is not causal, will it not be stable?

or these two properties independent of each other?

In this regard,please tell about both continuous and discrete time system

$\endgroup$
1
  • 2
    $\begingroup$ Stability and causality are orthogonal. $\endgroup$ – MBaz Sep 30 '19 at 13:54
4
$\begingroup$

They are independent of each other.

  • Continuous systems: For stability, the ROC (region of convergence) must include the jw-axis of the s-plane. Causal systems have a ROC which is a right-sided plane, with $Re(s)>\alpha$. Here $\alpha$ is the real part of the "most to the right" pole. Due to this, for a continuous system to be causal and stable, all its poles should be in the left half of the s-plane.
  • Discrete systems: For stability, the ROC must include the unitary circle of the Z-plane. Causal systems have a ROC of the form $|z|>\alpha$, where $\alpha$ is the modulus of the outermost pole of the system. Due to this, for a system to be causal and stable, all its poles must be inside the unit circle.
$\endgroup$
1
  • $\begingroup$ ,what do you mean?,to be stable, ROC should not contain poles ,either in discrete or continous system?? $\endgroup$ – engr Sep 30 '19 at 14:32

Not the answer you're looking for? Browse other questions tagged or ask your own question.