ABSTRACT
Stability of a system can be defined in many possible ways. The main reason for possible instability of this system is that although it is designed as negative feedback, it may turn out to be positive feedback if at some frequency a phase lags of 180° occurs in the loop. The frequency response of the open-loop system can therefore be utilized for investigating the stability of the closed-loop system. Unlike linear systems, the stability of nonlinear systems depends not only on the physical properties of the system but also on the magnitude and nature of the input as well as the initial conditions. Hence, the study of stability of nonlinear systems is more complicated than for linear systems. Several definitions of stability have been used in the literature for nonlinear systems. A. M. Lyapunov’s direct method provides a means for determining the stability of a system without actually solving for the trajectories in the state space.
