Abstract
In this paper we define a generalization of the gap metric for nonlinear systems. We prove two results which specialize to known results for linear systems. First, we show that a feedback system remains stable if the distance between the plant and its perturbation is less than the inverse of the norm of a certain parallel projection operator. Second, we show that every “continuously robust” metric on nonlinear systems is equivalent to the metric introduced in this paper.
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Dedicated to George Zames on the occasion of his 60th birthday
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© 1995 Springer-Verlag London Limited
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Georgiou, T.T., Smith, M.C. (1995). Metric uncertainty and nonlinear feedback stabilization. In: Francis, B.A., Tannenbaum, A.R. (eds) Feedback Control, Nonlinear Systems, and Complexity. Lecture Notes in Control and Information Sciences, vol 202. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0027672
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DOI: https://doi.org/10.1007/BFb0027672
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