Magnitude and phase envelopes of systems with affine linear uncertainty

TAN N. , Atherton D.

UKACC International Conference on Control 98, Swansea, United Kingdom, 1 - 04 September 1998, pp.1039-1044 identifier

  • Publication Type: Conference Paper / Full Text
  • Volume:
  • City: Swansea
  • Country: United Kingdom
  • Page Numbers: pp.1039-1044


In this note, firstly, the magnitude and phase extremums of a family of polynomials of the form P(s, q) = a(0)(q)+a(1)(q)s+.........+a(n)(q)s(n) whose coefficients depend linearly on q = [p(1),p(2),...,p(q)](T) and Q = {q : p(i)epsilon[<(p(i))under bar>,<(p(i))over bar>] i = 1, 2, ...., q} are obtained by using the geometric structure of the value set. Then the magnitude and phase extremums of this polynomial family multiplied with a fixed polynomial are investigated. Finally, a procedure is presented for computing the Bode envelopes of a control system with parametric uncertainty. The distinguishing feature of the results given in this paper is the efficient procedure introduced for constructing the 2q-convex parpolygon of P(s, q).