LMI-based Adaptive Observers for Nonlinear Systems

This paper deals with the design of adaptive observers that can estimate both the states and the parameters of a large class of nominal and perturbed nonlinear systems with a regression matrix (i.e. matching matrix with the unknown parameter vector) depending on unknown states. The asymptotic stability of the state and parameter estimate errors is developed in the presence of common persistency of excitation (PE). The observer gain calculus is cast as a linear matrix inequality (LMI) feasibility problem. The appeal of this proven theoretical design is further demonstrated numerically.