State observers of linear control systems with nonlinear outputs

Since the 1970s there has been an extensive study on the design of observers for nonlinear systems. Most current methods lead to the design of an exponential observer. As a necessary condition for the existence of an exponential observer, the linearized counterpart of the nonlinear system must be detectable. We consider control systems in a particular form. We try to understand under what conditions one can construct an exponential observer for this type of system. A typical example of such a system is using a mounted video camera to localize a robotic system. It is known that for the system we consider and in general for nonlinear systems, the observability does not only depend on the initial conditions, but also on the open-loop control. This presents an interesting issue: how to design a control strategy to maximize the observability. This has been a very important issue in the field of active perception in robotics. We present some initial results regarding this