Editing Instability (section)

==Instability in control systems==
{{See also|Stabilizability}}

In the theory of [[dynamical systems]], a [[state variable]] in a system is said to be unstable if it evolves without bounds. A system itself is said to be unstable if at least one of its state variables is unstable.

In [[continuous time]] [[control theory]], a system is unstable if any of the [[Root of a function|roots]] of its [[Characteristic equation (calculus)|characteristic equation]] has [[real part]] greater than zero (or if zero is a repeated root).  This is equivalent to any of the [[eigenvalues]] of the [[State space (controls)|state matrix]] having either real part greater than zero, or, for the eigenvalues on the imaginary axis, the algebraic multiplicity being larger than the geometric multiplicity.{{clarify|reason=what is the difference between these two types of multiplicity?|date=September 2015}} The equivalent condition in [[discrete time]] is that at least one of the eigenvalues is greater than 1 in absolute value, or that two or more eigenvalues are equal and of unit absolute value.