It is well known that an nth-order real polynomial D(z)= is Schur stable if its coefficients satisfy the monotonic condition, i.e., dn > dn-1 > > d1 > d0 > 0. In this letter it is shown that even if the monotonic condition is violated by one coefficient (say dk), D(z) is still Schur stable if the deviation of dk from dk+1 or dk-1 is not too large. More precisely we derive upper bounds for the admissible deviations of dk from dk+1 or dk-1 to ensure the Schur stability of D(z). It is also shown that the results obtained in this letter always yield the larger stability range for dk than an existing result.

Monotonic condition, a well-known sufficient condition for Schur stability of real polynomials, is relaxed. The condition reads that a series of strictly and monotonically decreasing positive coefficients of the polynomials yields Schur stability. It is shown by inspecting the original proof that equalities are allowed in all the inequalities but two which are located at appropriate positions.