Abstract
This short note discusses a notion of discontinuous feedback which is appealing from a theoretical standpoint because, on the one hand, solutions of closed-loop equations always exist, and on the other hand, if a system can be stabilized in any manner whatsoever, then it can be also stabilized in our sense. Moreover, the implementation of this type of feedback can be physically interpreted in terms of simple switching control strategies. A recent result obtained by the authors together with Clarke and Subbotin is described, which employs techniques from control-Lyapunov functions, nonsmooth analysis, and differential game theory in order to provide a general theorem on feedback stabilization.
Visiting Rutgers University. Supported in part by Russian Fund for Fundamental Research Grant 96-01-00219, by NSERC and La Fonde FCAR du Québec, and by the Rutgers Center for Systems and Control (SYCON)
Supported in part by US Air Force Grant AFOSR-94-0293
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Ledyaev, Y.S., Sontag, E.D. (1997). A notion of discontinuous feedback. In: Stephen Morse, A. (eds) Control Using Logic-Based Switching. Lecture Notes in Control and Information Sciences, vol 222. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0036087
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DOI: https://doi.org/10.1007/BFb0036087
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