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Robust Control of Positive Fractional‐Order Interconnected Systems with Heterogeneous Delays
Author(s) -
Le Hien Van,
Chu Kinh Trong
Publication year - 2019
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.1739
Subject(s) - control theory (sociology) , monotonic function , stability (learning theory) , mathematical optimization , robust control , controller (irrigation) , convex optimization , stability conditions , computer science , optimization problem , regular polygon , mathematics , control system , control (management) , engineering , artificial intelligence , electrical engineering , mathematical analysis , agronomy , statistics , geometry , discrete time and continuous time , machine learning , biology
The problem of robust decentralized control of positive fractional‐order interconnected systems with heterogeneous time‐varying delays is studied in this paper. Necessary and sufficient conditions are first derived for internal positiveness of the system. By exploiting the monotonicity induced from positivity of the system, robust stability conditions subject to uncertain system parameters are derived. The derived stability conditions are then utilized to address the controller synthesis problem. The design conditions for obtaining controller gains of stabilizing decentralized controllers are formulated using linear programming, which can be effectively solved by various convex optimization algorithms. Finally, the effectiveness of the obtained results is validated by two numerical examples.