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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