1 Describing Functions

In this article we define and overview the basic concept of a describing function, and then we look at a wide variety of usages and applications of this approach for the analysis and design of nonlinear dynamical systems. More specifically, the following is an outline of the contents: 1. concept and definition of describing functions for sinusoidal inputs (“sinusoidal-input describing functions”) and for random inputs (“random-input describing functions”) 2. traditional application of sinusoidal-input describing functions for limit cycle analysis, for systems with one nonlinearity 3. application of sinusoidal-input describing function techniques for determining the frequency response of a nonlinear system 4. application of random-input describing functions for the performance analysis of nonlinear stochastic systems 5. application of sinusoidal-input describing functions for limit cycle analysis, for systems with multiple nonlinearitie