Enhanced Dynamic Observer Design for the Disturbance‐Affected Nonlinear Parameter‐Varying Systems

ABSTRACT This article focuses on the topic of the generalized dynamic observer design for disturbance‐affected parameter‐varying (NLPV) systems. The objective is to develop a novel Linear Matrix inequality (LMI) condition designed to reduce the impact of the bounded exogenous signals (such as disturbances or noise) on the estimated state by exploiting the input‐to‐state stability (ISS) criterion. Two novel LMIs are derived in this paper by using the reformulated Lipschitz property of nonlinearities, Young's inequalities, upper boundary condition lemma, well‐known LPV approach, and two generalized matrix multipliers. The proposed LMIs encompass more decision variables than the existing LMIs due to the judicious deployment of these mathematical tools, especially matrix multipliers. Thus, these LMIs have enhanced feasibility over the existing ones, offering greater degrees of freedom for improved feasibility. A numerical example is employed to emphasize the effectiveness of the newly designed LMI‐based generalized dynamic observer.