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All the books I've used in my control systems class give a definition multiple-input, multiple-output systems and nonlinear systems, but all the techniques covered in the folloing chapters apply only to single variable LTI systems. The only occasions in which nonlinear systems are analyzed they are linearized from the very start in order to apply said techniques.

  1. What are some examples of real life situations in which one cannot use LTI systems, but rather a nonlinear or multivariable model?

  2. What sort of techniques are used to analyze these systems, and what sort of math is required to understand them?

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