Generalized Full Order Observer Subject to Incremental Quadratic Constraint (IQC) for a Class of Fractional Order Chaotic Systems

In this paper, we used Lyapunov theory and Linear Matrix Inequalities (LMI) to design a generalized observer by adding more complexity in the output of the dynamic systems. Our designed observer is based on the optimization problem, minimizing error between trajectories of master and slave systems s...

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Bibliographic Details
Published inFractal and fractional Vol. 6; no. 4; p. 189
Main Authors Marwan, Muhammad, Abidin, Muhammad Zainul, Kalsoom, Humaira, Han, Maoan
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.04.2022
Subjects
Algorithms
Calculus
Chaos theory
Design
dynamic systems
Dynamical systems
fractional order chaotic systems
incremental quadratic constraint
Linear matrix inequalities
Mathematical analysis
observer
Optimization
synchronization
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Summary:In this paper, we used Lyapunov theory and Linear Matrix Inequalities (LMI) to design a generalized observer by adding more complexity in the output of the dynamic systems. Our designed observer is based on the optimization problem, minimizing error between trajectories of master and slave systems subject to the incremental quadratic constraint. Moreover, an algorithm is given in our paper used to demonstrate a method for obtaining desired observer and gain matrixes, whereas these gain matrixes are obtained with the aid of LMI and incremental multiplier matrix (IMM). Finally, discussion of two examples are an integral part of our study for the explanation of achieved analytical results using MATLAB and SCILAB.
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ISSN:2504-3110
2504-3110
DOI:10.3390/fractalfract6040189