The method for determination of the stability of the feedback systems as a function of an adjustable gain parameter which does not provide detailed information concerning location of closed-loop poles as a function of gain K is called

The method for determination of the stability of the feedback systems as a function of an adjustable gain parameter which does not provide detailed information concerning location of closed-loop poles as a function of gain K is called Correct Answer Routh-Hurwitz criterion method

Root locus:

• This method is a graphical technique which gives the position of the roots of the characteristic equation as the gain K is varied.
• With root locus (unlike the case with Routh-Hurwitz criterion), we can do both analysis (i.e., for each gain value we know where the closed-loop poles are) and design (i.e., on the curve we can search for a gain value that results in the desired closed-loop poles).
• It is used for both continuous-time and a discrete-time system.

Nyquist plot:

• This method is mainly used for assessing the stability of a system with feedback.
• While Nyquist is a graphical technique, it only provides a limited amount of intuition for why a system is stable or unstable, or how to modify an unstable system to be stable.
• It can be used for both continuous-time and a discrete-time system but not directly a function of gain.

Routh-Hurwitz criterion:

• Using the Routh-Hurwitz method, the stability information can be obtained without the need to solve the closed-loop system poles.
• This can be achieved by determining the number of poles that are in the left-half or right-half plane and on the imaginary axis.
• It does not provide detailed information concerning the location of closed-loop poles as a function of gain K
• It is used to determine the absolute stability of a system.
• It is not a graphical technique.

Bode plot:

• A Bode plot is a graph of the magnitude (in dB) or phase of the transfer function versus frequency.
• It can be used for both continuous-time and a discrete-time system but not directly a function of gain.