Bode envelopes of multilinear affine systems

The paper deals with the problem of computing the Bode envelope of an uncertain transfer function whose numerator and denominator polynomials are multiples of independent uncertain polynomials of the form P(s, q) = l₀(q) + l₁(q)^s +.........+ l_n(q)sⁿ whose coefficients depend linearly on q = [q₁, q₂,..., q_q]^T and the uncertainty-box is Q = {q : q_i ϵ[q_i, q_i], i = 1,2,...., q}. Using the geometric structure of the value set of P(s, q), a powerful edge elimination procedure is proposed for computing the magnitude and phase envelopes of these uncertain systems. A numerical example is included to illustrate the benefit of the method presented.