Generation of frequency-response templates for linear systems with an uncertain time delay and multilinearly-correlated parameter perturbations

A simplicial algorithm is applied in this brief to generate frequency-response templates for a class of transfer functions having an uncertain time delay and multilinearly correlated parameter perturbations. It relies on developing a new zero-inclusion test algorithm for checking whether the origin is included in the image of a box T × Q = [τ^-, τ⁺] × Π _i=1^m-1[q_i^-, q_i ⁺] under a mapping of the form f (τ, q) = g(q) + h(q)e ^-jωτ, where g(q) and h(q) are multilinear complex-valued functions of q ∈ Q. We present easy-to-check sufficient conditions for the zero inclusion and exclusion of the value set f (T, Q). Using these sufficient conditions on subdivisions in the parameter box T × Q, we implement a branch-and-bound zero-inclusion test algorithm. To illustrate the proposed algorithm, we provide a numerical example