Some Necessary Conditions for Schur Stability of Polynomials
نویسنده
چکیده
This paper concerns the Schur stability of polynomials. Firstly necessary conditions are presented for the Schur stability of complex polynomials with fixed coefficients based on the discrete Hermite-Biehler theorem. Then the result is applied to obtain necessary conditions for the robust Schur stability of real interval polynomials.
منابع مشابه
Some Remarks on the -stability for Families of Polynomials
Using Brouwer degree, we prove a more general version of the zero exclusion principle for families of polynomials and apply it to obtain very simple proofs of extensions of recent results on the Routh-Hurwitz and Schur-Cohn stability of families of polynomials. 1. Introduction It is well know that the problem of the stability of a linear diierence or differential system with constant coeecients...
متن کاملOn Coefficient Diameters of Real Schur-stable Interval Polynomials
A new necessary, sharp condition for Schur-stability of real interval polynomials is established here. Moreover, a way to study perturbation effects on the coefficient range is outlined. The results may be used in a preprocessing rejection scheme when testing for robust Schur-stability.
متن کاملReflections on Schur-cohn Matrices and Jury-marden Tables and Classification of Related Unit Circle Zero Location Criteria*
We use the so-called reflection coefficients (RCs) to examine, review, and classify the Schur-Cohn and Marden-Jury (SCMJ) class of tests for determining the zero location of a discrete-time system polynomial with respect to the unit circle. These parameters are taken as a platform to propose a partition of the SCMJ class into four useful types of schemes. The four types differ in the sequence o...
متن کاملRobust Schur Stability of Interval Polynomials
In this note, different methods for the investigation of Schur stability of interval polynomials are considered and compared lo each other.
متن کاملThe Optimum Radius of the Robust Stability of Schur Polynomials
The problem of the Robust Stability of Schur Polynomials is investigated. Recently, a new approach based on Rouche's theorem of the classical complex analysis has been adopted for the solution of this problem. In this paper, an improvement of this solution is presented. This is the optimum solution of the Robust Stability problem of Schur Polynomials and is obtained by solving a minimization pr...
متن کامل