page_title: Nonlinear control
section_title: Nonlinear feedback analysis – The Lur'e problem
hierarchical_section_title: Nonlinear control / Nonlinear feedback analysis – The Lur'e problem
caption_attribution_description: English: Lur'e problem block diagram.
context_page_description: Nonlinear control theory is the area of control theory which deals with systems that are nonlinear, time-variant, or both. Control theory is an interdisciplinary branch of engineering and mathematics that is concerned with the behavior of dynamical systems with inputs, and how to modify the output by changes in the input using feedback, feedforward, or signal filtering. The system to be controlled is called the "plant". One way to make the output of a system follow a desired reference signal is to compare the output of the plant to the desired output, and provide feedback to the plant to modify the output to bring it closer to the desired output.
  Control theory is divided into two branches. Linear control theory applies to systems made of devices which obey the superposition principle. They are governed by linear differential equations. A major subclass is systems which in addition have parameters which do not change with time, called linear time invariant systems.
context_section_description: An early nonlinear feedback system analysis problem was formulated by A. I. Lur'e.
  Control systems described by the Lur'e problem have a forward path that is linear and time-invariant, and a feedback path that contains a memory-less, possibly time-varying, static nonlinearity.
  The linear part can be characterized by four matrices (A,B,C,D), while the nonlinear part is Φ(y) with  (a sector nonlinearity).
caption: Lur'e problem block diagram
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