# Relation between causality and stability? [closed]

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?

• Stability and causality are orthogonal.
– MBaz
Sep 30 '19 at 13:54

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.
• ,what do you mean?,to be stable, ROC should not contain poles ,either in discrete or continous system??
– engr
Sep 30 '19 at 14:32