Root counting and phase unwrapping with respect to the unit circle with applications Conference Paper

abstract

• In this paper we develop a new formula for counting the roots of a real polynomial inside the unit circle. This is done by representing the unit circle image of the polynomial in terms Tchebyshev polynomials, and the latter leads to a formula for the phase, unwrapped along the unit circle in terms of the zeros and signs of the Tcebyshev representation. This root counting formula can be specialized to yield a new interlacing condition for stability in terms of the Tchebyshev representation. The new formula is applied to the problem of constant gain stabilization of a digital control system and results in a determination of the entire set of stabilizing gains as a solution of sets of linear inequalities. Examples and future applications are discussed.

name of conference

• Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228)

authors

• Bhattacharyya, S

published proceedings

• PROCEEDINGS OF THE 40TH IEEE CONFERENCE ON DECISION AND CONTROL, VOLS 1-5

author list (cited authors)

• Keel, L. H., & Bhattacharyya, S. P.

citation count

• 1

complete list of authors

• Keel, LH||Bhattacharyya, SP

publication date

• January 2001

publisher

• Institute of Electrical and Electronics Engineers (IEEE)  Publisher

published in

• Proceedings of the ... IEEE Conference on Decision & Control / IEEE Control Systems Society. IEEE Conference on Decision & Control  Journal

Digital Object Identifier (DOI)

• 10.1109/cdc.2001.980393

International Standard Book Number (ISBN) 10

• 0-7803-7061-9

start page

• 3459

end page

• 3464

volume

• 4

URL

• http%3A%2F%2Fdx.doi.org%2F10.1109%2Fcdc.2001.980393