Around Problem 8.2: Image Extension of a Diffeomorphism
In this chapter, we study how a diffeomorphism can be extended to make its image cover the whole space, namely to make it surjective. In some cases, the construction of the extension is explicit and is illustrated on examples. In particular, this extension enables to guarantee the completeness of solutions to a high-gain observer written in the initial coordinates for a bioreactor.
- 1.Astolfi, D., Praly, L.: Output feedback stabilization for SISO nonlinear systems with an observer in the original coordinate. In: IEEE Conference on Decision and Control, pp. 5927–5932 (2013)Google Scholar
- 2.Bernard, P., Praly, L., Andrieu, V.: Expressing an observer in given coordinates by augmenting and extending an injective immersion to a surjective diffeomorphism (2018). https://hal.archives-ouvertes.fr/hal-01199791v6
- 6.Maggiore, M., Passino, K.: A separation principle for a class of non uniformly completely observable systems. IEEE Trans. Autom. Control 48 (2003)Google Scholar
- 7.Milnor, J.: Lectures on the \(h\)-Cobordism Theorem. Notes by L. Siebenmann and J. Sondow. Princeton University Press, Princeton (1965)Google Scholar