Estimation and control of a class of Euler discretized nonlinear systems

The observer and controller design for Euler discretized form of the following nonlinear systems: q= Ax+g(u, x) and y = Cx where x∈Rⁿ, u∈R^m, y∈R is presented. The nonlinearity g(u, x) has a triangular structure. It is shown that single output control affine systems which are observable for all inputs can be transformed locally almost everywhere, through a suitable change of coordinates into the form in which g(u, x) is linear in u. Low gain observer for these systems would require that at least part of the nonlinearity be taken into account in the design strategy.