# Routh Hurwitz Introduction

Cuthbert Nyack

Routh Hurwitz calculation gives information on the absolute instability of systems. It is based on the properties of the characteristic equation 1 + G(s) = 0.

Assuming the Characteristic Eqn can be written as shown below:-
Construct the table shown below using the eqn for b_{1} and c_{1}.
Instability can be inferred from the table. The number of roots in the RHS of the s plane are equal to the number of sign changes in the first column. Any sign change in the first column therefore means instability.

When enabled some of the applets appear as shown below. Some applets show how the coeffecients vary as a function of K. This gives an overview of how K affects the stability of the system.

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COPYRIGHT © 2006 Cuthbert Nyack.