Abstract
Minimax estimation is considered for a single-input single-output discrete-time uncertain system in the presence of bounded disturbance. The given regressors are divided into two sets which have small and large amplitudes respectively, where the amplitude ranges are assumed to be exclusive each other. Then, the nominal parameter of the system is estimated so that the maximal output error is minimized. The bounds of the disturbance and the parameter uncertainty are also estimated by using the output errors for these two sets. For this minimax estimation, the estimation errors are evaluated when the regressors of each set are persistently exciting. Furthermore, probabilistic estimation errors are derived when the regressors of each set are persistently exciting and periodic and have the same amplitude, and the disturbance and the parameter uncertainty are random variables which take their extreme values with a probability. The result implies that the errors converge to zero as the number of samples tends to infinity.
