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Robust stabilization of fractional‐order plant with general interval uncertainties based on a graphical method
Author(s) -
Zheng Shiqi,
Li Wenjie
Publication year - 2017
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.3979
Subject(s) - interval (graph theory) , bounding overwatch , mathematics , mathematical optimization , regular polygon , fractional programming , set (abstract data type) , polygon (computer graphics) , interval arithmetic , fractional order system , computer science , fractional calculus , mathematical analysis , combinatorics , telecommunications , physics , geometry , nonlinear system , artificial intelligence , quantum mechanics , frame (networking) , programming language , nonlinear programming , bounded function
Summary This paper concentrates on the robust stabilization of fractional‐order plant suffering from general interval uncertainties by using fractional‐order controllers. General interval uncertainties mean that the coefficients and orders of the denominator and nominator of the fractional‐order plant are all uncertain and lie in specified intervals. Two main contributions are presented, as follows. (i) Based on a graphical method, a necessary and sufficient criterion is proposed for the stabilization of the general interval fractional‐order plant. By adopting some well‐defined multivalue functions, the proposed method can explicitly construct the nonconvex boundary of the value set of the fractional system. (ii) Two alternative methods are presented to improve the computational efficiency of the stabilization test. Based on a newly developed redundancy elimination technique, the first method can avoid computing and plotting many segments, which are in the interior of the value set of the fractional system. The second method utilizes a novel convex polygon bounding approach. It can efficiently construct a convex polygon to bound the nonconvex value set of the general interval fractional system. Examples are followed to illustrate the effectiveness of the proposed methods.