Kharitonov's theorem is a result used in control theory to assess the stability of a dynamical system when the physical parameters of the system are not known precisely.
When the coefficients of the characteristic polynomial are known, the Routh–Hurwitz stability criterion can be used to check if the system is stable (i.e. if all roots have negative real parts).
Kharitonov's theorem can be used in the case where the coefficients are only known to be within specified ranges.
So it only takes four times more work to be informed about the stability of an interval polynomial than it takes to test one ordinary polynomial for stability.
Kharitonov's theorem is useful in the field of robust control, which seeks to design systems that will work well despite uncertainties in component behavior due to measurement errors, changes in operating conditions, equipment wear and so on.