Novel robust stability conditions of fractional-order systems with structured uncertain parameters based on parameter-dependent functions: the 0<α<1 case

作者：Chenfei Kang, Jun‐Guo Lu, Xuyi Qiu, Qing‐Hao Zhang · 发表于：International Journal of General Systems · 年份：2022 · DOI：10.1080/03081079.2022.2132489 · 被引用次数：3 · 研究领域：Fractional Differential Equations Solutions、Advanced Control Systems Design、Chaos control and synchronization

In this paper, the robust stability of fractional-order systems with fractional order 0<α<1 and structured uncertain parameters is considered. Firstly, novel robust stability conditions of the above systems are presented based on the parameter-dependent polynomial functions. Secondly, the existence of the parameter-dependent polynomial functions is transformed into linear matrix inequalities via the generalized Kalman-Yakubovič-Popov lemma. In addition, the above methods can also be applied to solve the robust stability of fractional-order systems with structured uncertainties or polytopic uncertainties. Finally, numerical examples are presented to show the proposed methods are less conservative than the existing methods.