Robust Stability by Path-Connectivity of Fractional Order Polynomials

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• 作者：J. A. López-Renteria ; G. Fernández-Anaya
• 关键词：Fractional order systems ; Fractional order polynomials ; Robust stability ; Path homotopy ; Stabilizing control
• 刊名：Acta Applicandae Mathematicae
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：145
• 期：1
• 页码：1-14
• 全文大小：966 KB
• 刊物主题：Mathematics, general; Computer Science, general; Theoretical, Mathematical and Computational Physics; Statistical Physics, Dynamical Systems and Complexity; Mechanics;
• 出版者：Springer Netherlands
• ISSN：1572-9036
• 卷排序：145

文摘

Given any pair of stable fractional order polynomials with fixed commensurate order \(\alpha \), for \(0<\alpha <2\), a stable path joining them is provided by mean of convex combinations in the arguments and magnitudes of their roots. It is shown that any pair of paths obtained with this technique are homotopically equivalent. Consequently, a dense trajectory in the stable fractional order polynomials set has been exhibited. Finally, a stabilizing feedback control in terms of the continuous coefficients of the path has been designed and an illustrative example is given.