Adaptive observer for a class of second order nonlinear systems

The problem addressed in this paper is the design of an adaptive observer that can estimate the states and identify the parameters of a class of second order nonlinear systems. The purpose of the proposed method is to eliminate the restrictive dissipativity condition from the stability proof that is present in many previous works presented in the literature. In this paper, the observer gain calculus is cast as a linear matrix inequality (LMI) feasibility problem. This formulation is therefore numerically tractable, but can also be solved analytically for the second order systems. Simulation results for state estimation and parameter identification of a one degree of freedom (1DOF) electromechanical rotary model are introduced to demonstrate the effectiveness of the designed algorithm.