Vertex-like design methods for systems with real parameter uncertainty

The author considers a single-input-single output plant family with affine real parameter uncertainty in the numerator and denominator of its transfer function. The objective is to design a compensator that guarantees robust stability and robust tracking. For tracking, the magnitude of the weighted sensitivity must be less than unity for all frequency and all parameter values. Vertex-like design methods are presented. It is shown that the robust design objectives are achieved if a compensator is found that simultaneously stabilizes a finite number of polynomials and guarantees that the magnitude of a finite number of weighted sensitivity-like functions is less that unity. In the case of a plant family with a single uncertainty the compensator is required to simultaneously stabilize four polynomials and satisfy magnitude bounds for four weighted sensitivity-like functions