The optimal control structure has been introduced as a design tool to measure the control-law nonlinearity of a given process design. In this context, control-law nonlinearity is the optimal degree of nonlinear compensation in the controller, a system property distinct from open-loop nonlinearity and determined by a performance objective and the region of operation as well as the nature of the open-loop system. This approach is extended to the analysis of multivariable systems with output feedback through the application of an extended Kalman filter. Coherence estimation is used as a practical method to measure continuous, open-loop multivariable system nonlinearity. The CSTR with van de Vusse kinetics, a system that features output feedback and a control-law nonlinearity that changes with operating points, is analyzed. The optimal control structure approach with coherence estimation correctly indicates changes in the control-law linearity between different operating points and changes as the regions of operation change around a particular operating point.