Reflection Coefficients of Polynomials and Stable Polytopes
Ülo Nurges · IEEE Transactions on Automatic Control · 2009
The geometry of stable discrete polynomials using their coefficients and reflection coefficients is investigated. Two linear Schur invariant transformations with a free parameter in the polynomial coefficient space are introduced. The first transformation Rfrntimes RfrrarrRfrnmaps an arbitrary stable polytope into another stable polytope. The second transformation Rfrntimes RfrrarrRfrnmaps a stable tilted n-dimensional hyperrectangle defined by the discrete Kharitonov theorem into a stable (n+1)- dimensional polytope.