In this study, we propose constructive ways to determine input‐to‐state stability (ISS) as well as incremental ISS (δISS) of nonpolynomial dynamical systems. The developed procedures are based on sums‐of‐square decomposition. This tool is only applicable to polynomial systems. Thus, a rational recast of the nonpolynomial system description is used. This recast generally leads to an increased system order and additional constraints. These constraints must be respected in the resulting formulations. The proposed approach gives a unique and constructive procedure to determine the ISS and the δISS property, which is normally nontrivial and needs a good understanding of the system's dynamics. The proposed approaches are illustrated on several examples.

中文翻译：

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确定非多项式系统的输入状态稳定性和增量输入状态稳定性

在这项研究中，我们提出了建设性的方式来确定输入状态稳定性（ISS）以及增量ISS（δ非多项式动力系统的ISS）。所开发的程序基于平方和分解。该工具仅适用于多项式系统。因此，使用了非多项式系统描述的合理重铸。此重铸通常会导致系统顺序增加和其他限制。在最终的配方中必须考虑这些限制。所提出的方法赋予了独特的，建设性的方法来确定ISS和δ ISS属性，它通常是平凡的，需要系统的动态特性有很好的了解。在几个示例中说明了所提出的方法。