The problem of robust oscillatory stability of uncertain systems is investigated in this article. For the uncertain systems, whose characteristic polynomial sets belong to the interval polynomial family or diamond polynomial family, sufficient and necessary conditions are given based on the stability and/or oscillation properties of some special extreme point polynomials. A systematic approach exploiting Yang's complete discrmination system is proposed to check the robust oscillatory stability of such uncertain systems. The proposed method is efficient in computation and can be easily implemented.
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