On the stability properties of polynomials with perturbed coefficients

Given a polynomialPc(S) = Sⁿ + t₁Sⁿ⁻¹ + ... tₙ = 0which is Hurwitz orPd(Z) = Zⁿ + t₁Zⁿ⁻¹ + ... tₙ = 0which has zeros only within or on the unit circle, it is of interest to know how much the coefficients tjcan be perturbed while preserving the stability properties. In this note, a method is presented for obtaining the largest hypersphere centered attT = [t₁ ... tₙ]containing only polynomials which are stable.