Observers for state-affine systems

A system whose discrete-time model is linear in state variables and nonlinear in control variables is considered. Under the assumption of generic observability (under single experiment) an exact observer algorithm is suggested. Also, it is shown that the existence of a general nonlinear asymptotic observer implies the existence of a linear one. Two design procedures for asymptotic observers are presented. Surprisingly, one of them extends to a rather complete solution for continuous-time systems with piecewise constant controls provided discrete output measurements are more frequent than switches of control values.