Characteristic Equation
From ControlTheoryPro.com

Contents
1 Introduction to the Characteristic Equation
The characteristic equation is a means of determining the closed loop poles of the system. For a system to be stable all the solutions to the characteristic equation must satisfy
Condition for Stability 
The characteristic equation is essential for pole placement controller design.
2 Characteristic Equation
The characteristic equation is defined by
Controller 
Plant 
Characteristic Equation 
To find the closed loop poles of the system solve for where .