Necessary and sufficient conditions for robustly oscillatory stability

The concept of robustly oscillatory stability for some uncertain systems is introduced in this paper. For some special uncertain systems, whose characteristic polynomial set can be seen as the interval polynomial family or diamond polynomial family, necessary and sufficient conditions are given based on the stability and/or oscillation properties of some special extreme point polynomials. A system implementation method using the complete discrimination system is provided to check the robustly oscillatory stability of such uncertain systems. The provided method is efficient in computation and can be easily realized by making use of the state-of-art symbol computation software such as MAPLE and MATLAB.