Parametric approach to robust stability with both parametric and nonparametric uncertainties

It is shown that the robust stability problem for a linear system with both parametric and nonparametric uncertainties is equivalent to a robust stability problem with parametric uncertainty only. This is achieved by converting the nonparametric uncertainty into a fictitious linear parameter. When applied to systems with affine parametric uncertainty and nonparametric uncertainty, the resulting robust stability problem involves bilinear parametric uncertainty which can be simply tested. This result is also useful in computing H_∞ norm and strict positive realness for systems with parametric uncertainty