Robustness of pole assignment of an interval polynomial using like λ-degree feedback gain based on the Kharitonov theorem

This work presents a robust scheme for a pole assignment of an interval polynomial in a damping-cone based on the Kharitonov theorem. Introducing a binomial coefficients (Like λ̃-degree) feedback gain, the robust stability is transformed into determining the condition under which all function values of the four families of the stability condition polynomials (SCP) are positive. The condition is that all of the leading coefficients of these SCP are positive. Moreover, a general formula for the generated entries of the Routh-Table of binomial coefficients (RTBC) is derived, verifying that all entries of the RTBC are positive. Finally, the problem of robustness of a pole assignment in a damping-cone is considered. Illustrative examples demonstrate the effectiveness of the proposed scheme.