I. Introduction
AN adaptive observer performs the role of state estimation as well as parameter identification. It comprises two coupled algorithms for the tasks. The state estimation algorithm works under unknown parameters, where updated parameters are used for estimating state variables. The parameter identification algorithm is also based on measured outputs and estimated states. Various adaptive observer methods have been introduced for nonlinear systems with unknown parameters [1]–[7]. For instance, an adaptive observer was developed for single input-single output nonlinear systems that can be transformed into a certain observable canonical form [1], where sufficient conditions for BIBS (bounded input-bounded state) stability were provided. For multi input-single output nonlinear systems that can be transformed into a special canonical form by a state-space change of coordinates, the observer gain matrix was obtained using the Meyer-Kalman-Yakubovic lemma [2], [3]. Recently adaptive observers for Lipschitz nonlinear systems were proposed [4], [5], where a quadratic stability condition was reformulated as a linear matrix inequality via a coordinate transformation [5].