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Admissible simulation relations, set-valued feedback, and controlled invariance

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Abstract

This work is a continuation of the author’s study of simulation relations between nonlinear input–output systems with disturbances. Previously we derived a criterion under which a “pointwise” simulation condition implies simulation by so-called “admissible” inputs and disturbances (that is, inputs and disturbances that yield time-dependent vector fields satisfying C 1 Carathéodory conditions). This criterion included a certain constant-rank assumption. In this paper we use the theory of set-valued mappings and differential inclusions to derive analogous results in which the constant-rank assumption is replaced by a compactness provision that augments the pointwise simulation condition. We illustrate our simulation results by deriving a sufficient condition for achieving global controlled invariance of a (possibly singular) nonlinear system through the use of a set-valued feedback law.

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Authors and Affiliations

  1. Department of Mathematics, University of Oklahoma, Norman, OK, 73019, USA

    Kevin A. Grasse

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  1. Kevin A. Grasse
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Correspondence to Kevin A. Grasse.

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Grasse, K.A. Admissible simulation relations, set-valued feedback, and controlled invariance. Math. Control Signals Syst. 20, 199–226 (2008). https://doi.org/10.1007/s00498-008-0030-3

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  • DOI: https://doi.org/10.1007/s00498-008-0030-3

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