Closed-loop pole: Difference between revisions

Revision as of 14:35, 27 August 2010

Revision as of 09:02, 13 February 2011

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The closed-loop poles, or eigenvalues, are obtained by solving the characteristic equation <math>{1+K\textbf{G}\textbf{H}}=0</math>. In general, the solution will be n complex numbers where n is the order of the [[characteristic polynomial]].

The preceedingpreceding is valid for single input single output systems (SISO). An extension is possible for multiple input multiple output systems, that is for systems where <math>\textbf{G}(s)</math> and <math>\textbf{K}(s)</math> are matrices whose elements are made of transfer functions. In this case the poles are the solution of equation:

<math>det(\textbf{I}+\textbf{G}(s)\textbf{K}(s))=0</math>