Robust stabilization of commensurate fractional order interval plants with PID controllers

Abstract

In this paper, we study robust stabilization of commensurate fractional order interval polynomial with the PID controller. In this paper, we show that a special class of commensurate fractional order interval plants can be stabilized by PID compensator if some of edge characteristic polynomials can be stabilized by the PID compensator. The proof is based on the fact that the special commensurate fractional order polytope of polynomial is robustly stable if and only if a small set of edge polynomials are robustly stable.