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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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>I</mi><mi>M</mi><mi>M</mi><mo>)</mo></mrow></semantics></math></inline-formula>. Finally, discussion of two examples are an integral part of our study for the explanation of achieved analytical results using MATLAB and SCILAB.