Measurement feedback controllers with constraints and their relation to the solution of Hamilton Jacobi inequalities

In this paper we propose a separation result for the stabilization of systems with control and measurement contraints, which clarifies the connection between the solution of a couple of Hamilton Jacobi inequalities (HJI) and the constraints imposed on the control and the estimation error fed back in the control loop. Once a solution of these HJI has been found a measurement feedback controller can be directly implemented. This controller has different features with respect to classical controllers: in classical control schemes an observer consists of a "copy" of the system plus a term proportional to the error between the actual measurement and the "estimated" measurement. Here, we allow a term which is a nonlinear function of this error.