Abstract
In this paper, for the purposes, first, of constructing nonlinear observers and, second, of output stabilization for observed nonlinear systems, we develop a theory allowing one to deal with singularities that can appear. In the uncontrolled analytic case, we are especially interested in finite singularities.
Using this theory, we generalize some of our previous results on the construction of nonlinear observers.
Next, we consider the theorem of a very interesting paper [26] and similar theorems of one of the authors. We prove a result containing all these previous ones; this result allows us to stabilize, via dynamic output feedback, certain nonlinear systems that were only state feedback stabilizable.
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Jouan, P., Gauthier, J.P. Finite singularities of nonlinear systems. Output stabilization, observability, and observers. Journal of Dynamical and Control Systems 2, 255–288 (1996). https://doi.org/10.1007/BF02259528
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DOI: https://doi.org/10.1007/BF02259528