Computation of the frequency response of multilinear affine systems

Tan N.

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, vol.47, no.10, pp.1691-1696, 2002 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 47 Issue: 10
  • Publication Date: 2002
  • Doi Number: 10.1109/tac.2002.803537
  • Journal Name: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1691-1696
  • Keywords: Bode envelope, frequency response, multilinear affine systems, Nichols envelope, Nyquist envelope, UNCERTAIN SYSTEMS, ROBUST STABILITY, INTERVAL, ALGORITHM
  • Inonu University Affiliated: Yes

Abstract

This note deals with the problem of computing the frequency response of an uncertain transfer function whose numerator and denominator polynomials are multiples of independent uncertain polynomials of the form P(s, q) = l(0) (q) + l(1) (q) s + ... + l(n) (q) s(n) whose coefficients depend linearly on q = [q(1), q(2),...,q(q)](T) and the uncertainty box is Q = {q: q(i) is an element of [q(i), q(i)], i = 1, 2,..,q}. Using the geometric structure of the value set-of P(s, cl), a powerful edge elimination procedure is proposed for computing the Bode, Nyquist, and Nichols envelopes of these uncertain systems. A numerical example is included to illustrate the benefit of the method presented.