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Design of unknown‐input reduced‐order observers for a class of nonlinear fractional‐order time‐delay systems
Author(s) -
Huong Dinh Cong,
Thuan Mai Viet
Publication year - 2018
Publication title -
international journal of adaptive control and signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.73
H-Index - 66
eISSN - 1099-1115
pISSN - 0890-6327
DOI - 10.1002/acs.2852
Subject(s) - lipschitz continuity , control theory (sociology) , mathematics , nonlinear system , observer (physics) , stability (learning theory) , quadratic equation , exponential stability , fractional calculus , linear matrix inequality , mathematical optimization , computer science , mathematical analysis , control (management) , physics , geometry , quantum mechanics , artificial intelligence , machine learning
Summary This paper considers the design of reduced‐order state observers for fractional‐order time‐delay systems with Lipschitz nonlinearities and unknown inputs. By using the Razumikhin stability theorem and a recent result on the Caputo fractional derivative of a quadratic function, a sufficient condition for the asymptotic stability of the observer error dynamic system is presented. The stability condition is obtained in terms of linear matrix inequalities, which can be effectively solved by using existing convex algorithms. Numerical examples and simulation results are given to illustrate the effectiveness of the proposed design approach.