Observability of Nonlinear Input-Affine Systems
نویسندگان
چکیده
The main aim of this paper is to characterize the set of states indistinguishable from a given state of a general nonlinear input-affine control system with complete and smooth vector fields and smooth output functions. For this purpose, we introduce the extended observation space, and show that the set of states indistinguishable from a given state is the intersection of level sets containing that state, of functions from the extended observation space. A partial relationship between the annihilator of the extended observation space and the set of states indistinguishable from a given state is also established. In the case of an analytic system, the observation space considered in the literature and extended observation space introduced here are essentially the same.
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