Damping margins of polynomials with perturbed coefficients

Considers the polynomial P(s)=t₀ Sⁿ+t₁ S^n-1 +···+t_n where 0<a _j⩽t_j⩽b_j. Recently, V.L. Kharitonov (1978) derived a necessary and sufficient condition for this polynomial to have only zeros in the open left-half plane. Two lemmas are derived to investigate the existence of theorems similar to the theorem of Kharitonov. Using these lemmas, the theorem of Kharitonov is generalized for P(s) to have only zeros within a sector in the complex plane. The aperiodic case is also considered