Closed-loop pole: Difference between revisions

Revision as of 18:43, 28 June 2016

Revision as of 05:49, 3 July 2016

Line 16:

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 preceding 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 the equation

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