Open AccessPerformance analysis and control of fractional‐order positive systems
Author(s) -
Wang Cuihong,
Zhao Yafei
Publication year - 2019
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2018.5225
Subject(s) - mathematics , interval (graph theory) , control theory (sociology) , positive systems , norm (philosophy) , stability theory , order (exchange) , diagonal , linear system , state (computer science) , control (management) , nonlinear system , computer science , mathematical analysis , algorithm , combinatorics , physics , geometry , finance , artificial intelligence , quantum mechanics , law , political science , economics
Unlike a general integer‐order linear system, the L 1 and L 2 norms of its state and output variables may not be convergent in an infinite time interval even if the concerned fractional‐order linear system is asymptotically stable or even Mittag–Leffler stable. Therefore, this study mainly investigates the analysis and synthesis of L 1 and L 2 performances in a finite time interval for a class of fractional‐order positive systems. The L ∞ performance problem in the infinite time interval is also concerned since the boundness of the L ∞ norm of the state and output variables can be guaranteed in the infinite time interval if the concerned fractional‐order positive system is asymptotical stable. The L 1 and L ∞ performance characterisations are expressed by linear programming and L 2 performance characterisation is expressed in terms of linear matrix inequality with a diagonal positive definite solution. Based on these performance conditions, the problems of stabilisation by a state feedback controller with L p( p ∈ { 1 , 2 , ∞ } ) ‐gain guaranteed are solved for fractional‐order positive systems. An example is presented to show the effectiveness of the proposed methods in this study.