document: Phase conditions for Schur polynomials The rate of change of phase of a real or complex Schur polynomial , evaluated along the unit circle traversed counterclockwise , is strictly positive . For polynomials with real coefficients , this bound can be tightened . These and some other fundamental bounds on the rate of change of phase are derived here , using the Tchebyshev representation of the image of a real polynomial evaluated on the unit circle
doc_bio_tags: B I O O O O B I I I I O O O O O B I O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O B I I I I O O O O O O B I O O O O O O O O O O O O
extractive_keyphrases: phase conditions schur polynomial real coefficients rate of change of phase tchebyshev representation
abstractive_keyphrases: phase monotonicity robust stability discrete-time control systems stabilization