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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 178718, 10 pages
Research Article

State Estimation for Fractional-Order Complex Dynamical Networks with Linear Fractional Parametric Uncertainty

College of Mathematics and Information and Engineering, Jiaxing University, Zhejiang, 314001, China

Received 30 October 2012; Revised 8 February 2013; Accepted 13 February 2013

Academic Editor: Juan J. Trujillo

Copyright © 2013 Hongjie Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper deals with state estimation problem for a class of fractional-order complex dynamical networks with parametric uncertainty. The parametric uncertainty is assumed to be of linear fractional form. Firstly, based on the properties of Kronecker product and the stability of fractional-order system, a sufficient condition is derived for robust asymptotic stability of linear fractional-order augmented system. Secondly, state estimation problem is then studied for the same fractional-order complex networks, where the purpose is to design a state estimator to estimate the network state through available output measurement, the existence conditions of designing state estimator are derived using matrix's singular value decomposition and LMI techniques. These conditions are in the form of linear matrix inequalities which can be readily solved by applying the LMI toolbox. Finally, two numerical examples are provided to demonstrate the validity of our approach.