Input-Output Analysis

  • Shankar Sastry
Part of the Interdisciplinary Applied Mathematics book series (IAM, volume 10)


In this chapter we introduce the reader to various methods for the input-output analysis of nonlinear systems. The methods are divided into three categories:
  1. 1.

    Optimal Linear Approximants for Nonlinear Systems. This is a formalization of a technique called the describing function technique, which is popular for a quick analysis of the possibility of oscillation in a feedback loop with some nonlinearities in the loop.

  2. 2.

    Input-output Stability. This is an extrinsic view to the stability of nonlinear systems answering the question of when a bounded input produces a bounded output. This is to be compared with the intrinsic or state space or Lyapunov approach to stability in the next two chapters.

  3. 3.

    Volterra Expansions for Nonlinear Systems. This is an attempt to derive a rigorous “frequency domain” representation of the input output behavior of certain classes of nonlinear systems.



Nonlinear System Convolution Kernel Bilinear System Volterra Series Linear Time Invariant System 
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Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Shankar Sastry
    • 1
  1. 1.Department of Electrical Engineering and Computer ScienceUniversity of California, BerkeleyBerkeleyUSA

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