Robust stability analysis for a class of polynomial family with polynomial perturbation parameters is considered.Based on linear matrix inquality(LMI)

a stability criterion is presented for the class of polynomial family.Moreover

a method is also provided to estimate the maximal stability domain.Since an analytic function can be arbitrary approximated by a polynomial

the provided methods can be applied to robust stability analysis of polynomial family with general non-linear perturbation parameters.Finally

an illustrative example is given to show the feasibility of the methods in practice.