Editing Control theory (section)

==Linear and nonlinear control theory==
The field of control theory can be divided into two branches:
* ''[[Linear control theory]]'' – This applies to systems made of devices which obey the [[superposition principle]], which means roughly that the output is proportional to the input.  They are governed by [[linear differential equation]]s.  A major subclass is systems which in addition have parameters which do not change with time, called ''[[linear time invariant]]'' (LTI) systems.   These systems are amenable to powerful [[frequency domain]] mathematical techniques of great generality, such as the [[Laplace transform]], [[Fourier transform]], [[Z transform]], [[Bode plot]], [[root locus]], and [[Nyquist stability criterion]].  These lead to a description of the system using terms like [[Bandwidth (signal processing)|bandwidth]], [[frequency response]], [[eigenvalue]]s, [[gain (electronics)|gain]], [[resonant frequency|resonant frequencies]], [[zeros and poles]], which give solutions for system response and design techniques for most systems of interest. 
* ''[[Nonlinear control theory]]'' – This covers a wider class of systems that do not obey the superposition principle, and applies to more real-world systems because all real control systems are nonlinear.  These systems are often governed by [[nonlinear differential equation]]s.  The few mathematical techniques which have been developed to handle them are more difficult and much less general, often applying only to narrow categories of systems.  These include [[limit cycle]] theory, [[Poincaré map]]s, [[Lyapunov function|Lyapunov stability theorem]], and [[describing function]]s.  Nonlinear systems are often analyzed using [[numerical method]]s on computers, for example by [[simulation|simulating]] their operation using a [[simulation language]].  If only solutions near a stable point are of interest, nonlinear systems can often be [[linearization|linearized]] by approximating them by a linear system using [[perturbation theory]], and linear techniques can be used.<ref>{{cite web| url = http://www.mathworks.com/help/toolbox/simulink/slref/trim.html| title = trim point}}</ref>