Nonlinear Control - Analysis and Control of Nonlinear Systems

Analysis and Control of Nonlinear Systems

There are several well-developed techniques for analyzing nonlinear feedback systems:

  • Describing function method
  • Phase plane method
  • Lyapunov stability analysis
  • Singular perturbation method
  • Popov criterion (described in The Lur'e Problem below)
  • Center manifold theorem
  • Small-gain theorem
  • Passivity analysis

Control design techniques for nonlinear systems also exist. These can be subdivided into techniques which attempt to treat the system as a linear system in a limited range of operation and use (well-known) linear design techniques for each region:

  • Gain scheduling

Those that attempt to introduce auxiliary nonlinear feedback in such a way that the system can be treated as linear for purposes of control design:

  • Feedback linearization

And Lyapunov based methods:

  • Lyapunov redesign
  • Nonlinear damping
  • Backstepping
  • Sliding mode control

Read more about this topic:  Nonlinear Control

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