ABSTRACT
Nonlinearities in the actuator, feedback path, and plant are reviewed. The following concepts are developed: limit cycles, stability of linearized systems, conditional stability, global stability, and absolute stability. Nonlinear dynamic compensators, which ensure absolute stability without penalizing the available feedback, are introduced. In a nondynamic link, the current value of the output variable depends only on the current value of the input variable and not on its previous values. The first Lyapunov method for stability analysis is applicable to nonlinear systems with differentiable characteristics. The Lyapunov function is often constructed as a sum of a quadratic form of the system variables and an integral of a nonlinear static function reflecting the system nonlinearity. Signals that are initially finite and then, when the time increases, remain within an envelope whose upper and lower boundaries asymptotically approach zero are called vanishing. The Popov criterion can be understood through the mathematical analogy between the feedback system and the connection of electrical two-poles.
