Nonlinear control is the area of control engineering specifically involved with systems that are nonlinear, time-variant, or both. Many well-established analysis and design techniques exist for linear time-invariant (LTI) systems (e.g., root-locus, Bode plot, Nyquist criterion, state-feedback, pole placement); however, one or both of the controller and the system under control in a general control system may not be an LTI system, and so these methods cannot necessarily be applied directly. Nonlinear control theory studies how to apply existing linear methods to these more general control systems. Additionally, it provides novel control methods that cannot be analyzed using LTI system theory. Even when LTI system theory can be used for the analysis and design of a controller, a nonlinear controller can have attractive characteristics (e.g., simpler implementation, increased speed, or decreased control energy); however, nonlinear control theory usually requires more rigorous mathematical analysis to justify its conclusions.
Read more about Nonlinear Control: Properties of Nonlinear Systems, Analysis and Control of Nonlinear Systems, Nonlinear Feedback Analysis – The Lur'e Problem, Further Reading
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