On Local Observer Design for LQR Problems with Tracking

The paper addresses the problem of an observer design for a nonlinear system for which a linear approach is followed for the control synthesis. The linear context driven by the control design allows to focus the observers design in the class of local, i.e. linear, observers. It is shown that when the control contains an external reference, the solution obtained working with the linear approximation to get local solutions produces non consistent results in terms of local regions of convergence for the system and for the observer. The case of a control law which solves a LQR problem with tracking is addressed and two different approaches with respect to the classical one for the observer design are studied. The results are applied to an epidemic spread control to check the differences in the performances for the two different approaches.