On the Design of Adaptive Observers for Persidskii Systems

This paper presents the design of an adaptive observer for simultaneous state estimation and parametric identification in Persidskii systems. The main assumption is that the relative degree of the system is equal to one, which allows certain matching conditions for both linear and nonlinear outputs of the system to be satisfied. The known nonlinearities are assumed to be monotone and satisfy sector condition, while the regressor associated with the unknown parameters is Lipschitz continuous. For this type of system, the adaptive observer is designed considering the presence of disturbances and measurement noise. Input-to-state stability conditions are established through Lyapunov analysis. The validity of the proposed observer is illustrated by numerical examples.