Ultimately Periodic Behavior in a Class of Non-Linear Servomechanisms

Abstract

This chapter discusses periodic behavior in a class of nonlinear servomechanisms. It describes the general class of servomechanisms, which is comprised of s(·) as given signal, F(·) as a non-linear function, and k(·) as the impulse response of a linear system. This class is studied by finding a fixed point in a specific set of a function space. Thus, many properties of the class are established without either specifying s(·), F(·), and k(·) in detail or solving the equation explicitly. The function k(·) is impulse response of a physically realizable network, which vanishes for negative argument, and is absolutely integrable. As the function space and the set in which the fixed point is found should be chosen in many ways, the method described in the chapter is used for a wide variety of problems. The choice to be made depends on the equation to be treated and on the properties of the solution that are of interest.