Extended Luenberger observer for non-linear multivariable systems

Abstract

For non-linear multiple-input multiple-output systems [xdot] = f(x, u), y = h(x, u), nonlinear observers are designed using a transformation into the non-linear observer canonical form and an extended linearization. The differential equation of observer error in canonical coordinates is linearized about the reconstructed trajectory, and dimensioned by eigenvalue assignment. With reference to the extended Kalman filter algorithm, this non-linear observer design is called the extended Luenberger observer. This observer design is possible for all sufficiently smooth and locally observable systems. In comparison with single-output systems, the non-linear observer design can be essentially simplified using the degrees of freedom available in the case of multiple outputs.