What is a `large´ number of parameters in robust systems?

The authors consider the robust stability analysis of a characteristic polynomial p(s,q) whose coefficients are functions of l uncertain bounded parameters in the vector q=[q₁ q₂ . . . q_l]∈Q. There is an important class of tree-structured polynomials for which the value set p(j ω,q) can be constructed in consecutive steps via a two-at-a-time procedure. A mechanical system is modeled in such a way that a tree structure is present. A minimum-phase stable compensator with uncertain parameters is considered. For the resulting polynomial with multilinear dependence on q∈R¹³, the robustness analysis is shown to be very fast. Since computation of the value set at each frequency takes 0.6 seconds on an Apollo 3500 workstation, a `movie´ with ω as animation time was produced. Thus l=13 is not a large number for this class of systems