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H ∞ Model Reduction for Positive Fractional Order Systems
Author(s) -
Shen Jun,
Lam James
Publication year - 2014
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.694
Subject(s) - mathematics , parameterized complexity , bounded function , reduction (mathematics) , variable (mathematics) , linear matrix inequality , matrix (chemical analysis) , norm (philosophy) , order (exchange) , control theory (sociology) , mathematical optimization , algorithm , computer science , mathematical analysis , control (management) , materials science , geometry , finance , artificial intelligence , political science , law , economics , composite material
This paper focuses on the H ∞ model reduction problem of positive fractional order systems. For a stable positive fractional order system, we aim to construct a positive reduced‐order fractional system such that the associated error system is stable with a prescribed H ∞ performance. Then, based on the bounded real lemma for fractional order systems, a sufficient condition is given to characterize the model reduction problem with a prescribed H ∞ ‐norm error bound in terms of a linear matrix inequality ( LMI ). Furthermore, by introducing a new flexible real matrix variable, the desired reduced‐order system matrices are decoupled with the complex matrix variable and further parameterized by the new matrix variable. A corresponding iterative LMI algorithm is also proposed. Finally, several illustrative examples are given to show the effectiveness of the proposed algorithms.