Towards Enhancing Nonlinear Observers for Lipschitz System: Exploiting
the Matrix Multipliers-based LMIs
Abstract
This 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 H ∞ criterion, while the second one utilises
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.