Toward enhancing nonlinear observers for Lipschitz system: Exploiting the matrix multipliers‐based LMIs

Abstract

AbstractThis article is focused on the design of an LMI‐based observer for the class of disturbance‐affected nonlinear systems. Two novel LMI conditions are derived by deploying a more general form of the matrix multiplier compared to the one used in the literature. The first method is based on the use of the criterion, while the second one utilizes an ISS notion. Both LMIs are developed by employing the reformulated Lipschitz property, a well‐known LPV approach and the new variant of Young inequality. The key element of the proposed LMI conditions is the incorporation of the novel matrix multipliers which allow us to include some additional decision variables as compared to the methods proposed in the literature. These additional variables add extra degrees of freedom, thus enhancing the LMI feasibility. Furthermore, the effectiveness of the proposed methodologies is showcased through a numerical example.