Application of Kharitonov´s Theorem to Mechanical Systems

In this note we apply Kharitonov´s theorem to derive a robust stability condition for 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. We describe a simple procedure for designing PID controllers for these mechanical systems and prove 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.