It determines the poles of a characteristic equation with respect to the left and right half of the *s-*plane without solving the equation. The transfer function of any closed loop system is given by:

In Eq. (8.1) *a* and *b* are constants. To find the poles of this closed loop system put

The roots of this characteristic equation represent the closed loop poles. The stability of the system depends on these poles.

The necessary but not sufficient conditions for the system having no roots in right half of *s*-plane are given below:

- All the co-efficient of the polynomial must ...

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