Application of Kharitonov´s theorem to mechanical systems

Kharitonov´s theorem is used to derive a robust stability condition for proportional-integral-derivative (PID)-controlled multi-degree-of-freedom mechanical systems. The characteristic equation of such a system is given as a determinant of a third-order polynomial with matrix coefficients from which a scalar interval polynomial is obtained. A simple procedure for designing PID controllers for these mechanical systems is described, and a new Kharitonov-like result which states roughly that a controller designed for an upper bounding inertia matrix results in stable set-point regulation for all other inertias is proved