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Nyquist stability criterion
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<p>In <a href="/facts/Control_theory/aIuERpn6">control theory</a> and <a href="/facts/Stability_theory/Su5sHnxs">stability theory</a>, the Nyquist stability criterion or Strecker–Nyquist stability criterion, independently discovered by the German electrical engineer Felix Strecker [de] at <a href="/facts/Siemens/coa80TQn">Siemens</a> in 1930 and the Swedish-American electrical engineer <a href="/facts/Harry_Nyquist/BIDzoc9I">Harry Nyquist</a> at <a href="/facts/Bell_Telephone_Laboratories/fKP5Gk0H">Bell Telephone Laboratories</a> in 1932, is a graphical technique for determining the <a href="/facts/Stability_criterion/AMSTVwWT">stability</a> of a <a href="/facts/Dynamical_system/782gREl5">dynamical system</a>. </p><p>Because it only looks at the Nyquist plot of the <a href="/facts/Open-loop_controller/vjRIkFzd">open loop systems</a>, it can be applied without explicitly computing the <a href="/facts/Poles_and_zeros/gnA3U8VP">poles and zeros</a> of either the closed-loop or open-loop system (although the number of each type of right-half-plane <a href="/facts/Singularity_(mathematics)/Y5sMQY4I">singularities</a> must be known). As a result, it can be applied to systems defined by non-<a href="/facts/Rational_function/2nJGu0Ko">rational functions</a>, such as systems with delays. In contrast to <a href="/facts/Bode_plot/xcF1ej98">Bode plots</a>, it can handle <a href="/facts/Transfer_function/slDsh1lH">transfer functions</a> with right half-plane singularities. In addition, there is a natural generalization to more complex systems with <a href="/facts/Multiple-input_multiple-output_system/1EXPB7Vl">multiple inputs and multiple outputs</a>, such as control systems for airplanes. </p><p>The Nyquist stability criterion is widely used in <a href="/facts/Electronics/E4JhgISq">electronics</a> and <a href="/facts/Control_system_engineering/5ckfXmB8">control system engineering</a>, as well as other fields, for designing and analyzing systems with <a href="/facts/Feedback/XnuWH3zp">feedback</a>. While Nyquist is one of the most general stability tests, it is still restricted to <a href="/facts/Linear_time-invariant/kEmj0QDC">linear time-invariant</a> (LTI) systems. Nevertheless, there are generalizations of the Nyquist criterion (and plot) for non-linear systems, such as the <a href="/facts/Circle_criterion/EScnVdJ5">circle criterion</a> and the scaled relative graph of a <a href="/facts/Nonlinear_operator/Q1PBKNVV">nonlinear operator</a>. Additionally, other <a href="/facts/Stability_criterion/AMSTVwWT">stability criteria</a> like <a href="/facts/Lyapunov_stability/r3je5zaQ">Lyapunov methods</a> can also be applied for non-linear systems. </p><p>Although Nyquist is a graphical technique, it only provides a limited amount of intuition for why a system is stable or unstable, or how to modify an unstable system to be stable. Techniques like <a href="/facts/Bode_plots/xcF1ej98">Bode plots</a>, while less general, are sometimes a more useful design tool. </p>