Sampled measurement adaptive observer for a class of state-affine nonlinear

The problem of state observation, based on sampled output measurements, is addressed for a class of nonlinear state-affine systems. The difficulty lies in the fact that the state equation involve the undisturbed output with unknown parameters. A hybrid adaptive observer is designed and formally analysed. Sufficient conditions are established for the observer to be exponentially convergent in the absence of output disturbance. The sufficient conditions include a usual persistent excitation condition as well as an explicit upper bound on the admissible sampling time. In presence of nonzero disturbance, the L∞-gain between the disturbance input and the (state and parameter) estimation errors is explicitly established in function of the design parameters.