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 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.

Automated summary

In this paper, we designed a generalized observer using Lyapunov theory and Linear Matrix Inequalities (LMI) to add complexity in the output of dynamic systems. By minimizing the trajectory error between master and slave systems, subject to incremental quadratic constraint, our observer is optimized. We provided an algorithm for obtaining desired observer and gain matrixes using LMI and incremental multiplier matrix (IMM), and discussed two examples to demonstrate the achieved analytical results through MATLAB and SCILAB.