Simple proof of stability criterion for interval quasi-polynomials

In this study, the authors study the stability of interval quasi-polynomials with fixed delay and interval delay. The stability of quasi-polynomial with a fixed coefficient can be checked by a frequency characteristic plot. The vertex quasi-polynomials with fixed coefficients are defined. Two theorems are presented to determine the stability of interval quasi-polynomials. Stability of interval quasi-polynomials with fixed delay or interval delay may be determined by eight or 16 vertex quasi-polynomials. The example is given to illustrate the proposed method.