Nonlinear Observer Design in Discrete-time Systems: Incorporating LMI Relaxation Strategies

Abstract

This manuscript focuses on the $\mathcal{H}_\infty$ observer design for a class of nonlinear discrete systems under the presence of measurement noise or external disturbances. Two new Linear Matrix Inequality (LMI) conditions are developed in this method through the utilization of the reformulated Lipschitz property, a new variant of Young inequality and the well-known Linear Parameter Varying (LPV) approach. One of the key components of the proposed LMIs is the generalized matrix multipliers. The judicious use of these multipliers enables us to introduce more numbers of decision variables inside LMIs than the one illustrated in the literature. It aids in adding some extra degrees of freedom from a feasibility point of view, thus enhancing the LMI conditions. Thus, the established LMIs are less conservative than existing ones. Later on, the effectiveness of the developed LMIs and observer is highlighted through a numerical example and the application of state of charge (SoC) estimation in the Li-ion battery model.