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Uniting local and global observers for the state estimation of nonlinear continuous-time systems

Generic techniques are available for the design of local observers for nonlinear continuous-time systems. By local, we mean that the state estimate is guaranteed to converge to the true state, provided its initial value is nearby the plant initial condition. The main drawback of this approach is the right initialization of the observer, which may not be easy in practice. To overcome this potential issue, we propose to combine two observers: a local one, and an other observer, which provides (approximate) estimates but in a global sense, namely for any initial condition. We explain how to combine these two observers with a hybrid scheme guaranteeing global asymptotic convergence. The hybrid observer, called uniting observer, matches the local observer when the initial conditions are nearby the initial conditions of the observed system. We illustrate the proposed approach by means of a numerical example.