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New Results on Stabilization of Fractional‐Order Nonlinear Systems via an LMI Approach
Author(s) -
Thuan Mai Viet,
Huong Dinh Cong
Publication year - 2018
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.1644
Subject(s) - control theory (sociology) , nonlinear system , mathematics , linear matrix inequality , lyapunov function , fractional calculus , quadratic equation , regular polygon , mathematical optimization , computer science , control (management) , physics , geometry , quantum mechanics , artificial intelligence
This paper considers the systematic design of robust stabilizing state feedback controllers for fractional‐order nonlinear systems. By using the Lyapunov direct method and a recent result on the Caputo fractional derivative of a quadratic function, stabilizability conditions expressed in terms of linear matrix inequalities are derived. The controllers can then be derived by using existing computationally effective convex algorithms. Two numerical examples with simulation results are provided to demonstrate the effectiveness of our results.