The correct answer is: A. Nyquist Criterion
The Nyquist criterion is a method for determining stability in linear time-invariant (LTI) systems. It is based on the idea that the frequency response of a stable system must encircle the point (-1,0) in the complex plane an even number of times. However, the Nyquist criterion is not applicable to nonlinear systems because the frequency response of a nonlinear system is not necessarily a single-valued function of frequency.
Quasi linearization is a technique for approximating a nonlinear system with a linear system. This can be done by Taylor expanding the nonlinear function around a particular operating point and then linearizing the resulting expression. Quasi linearization can be used to analyze the stability of a nonlinear system, but it is not as accurate as other methods, such as the Lyapunov method.
Functional analysis is a branch of mathematics that studies the properties of functions and functional spaces. Functional analysis can be used to analyze the stability of nonlinear systems, but it is a very complex and technical subject.
Phase-plane representation is a graphical method for analyzing the dynamics of a nonlinear system. In phase-plane representation, the state variables of the system are plotted on a two-dimensional plane. The trajectories of the system in the phase plane can be used to determine the stability of the system.
In conclusion, the Nyquist criterion is not applicable to nonlinear systems because the frequency response of a nonlinear system is not necessarily a single-valued function of frequency.