Around Problem 8.1: Augmenting an Injective Immersion into a Diffeomorphism

  • Pauline BernardEmail author
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 479)


This chapter addresses the question of the extension of an injective immersion into a diffeomorphism. This is done by complementing continuously the full-rank rectangular Jacobian of the injective immersion into an invertible square matrix. Indeed, when this is possible, an explicit formula for the diffeomorphism is given. Several sufficient conditions for a Jacobian complementation are given with either explicit formulas or constructive algorithms and are illustrated in the example of an oscillator with unknown frequency.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Electrical, Electronic, and Information Engineering “Guglielmo Marconi”University of BolognaBolognaItaly

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