Verify stability of the system [closed]

1. How do you find the stability of a closed loop system?
2. How do you prove stability of a system?
3. What makes a closed loop system unstable?
4. Which is stable closed loop or open-loop?

How do you find the stability of a closed loop system?

A closed loop system is stable when all its eigenvalues have positive real part. Incidentally, poles of are same as zeros of . This means for stability, number of zeros of in the right half of the complex plane must be zero.

How do you prove stability of a system?

If all the poles lie in the left half of the s-plane, then the system is stable. 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 makes a closed loop system unstable?

The closed-loop system is unstable because two roots of the characteristic equation have positive real parts. We arbitrarily assume that an > 0. If an < 0, we multiply Equation 6 by -1 to generate a new equation that satisfies this condition.

Which is stable closed loop or open-loop?

As compared to closed loop system an open loop control system is more stable as all its roots are in left half of s plane only, but it less accurate since there is no feedback to measure the output value and compare it with the input value.