Consider the following nonlinear system
[Formula Omitted]
where ϰ ∈ Rⁿ, f, ℊ₁,…,ℊｍ are C∞ function in Rⁿ and ℎ is a C∞ function in R⍴, all defined on a neighborhood of 0. The problem of finding a necessary and sufficient condition such that system (1) can be transformed to a linear controllable system by a state coordinate change and feedback has been studied
quite well. In this thesis, we first discuss a few different approaches to this problem and eventually we will show that the slightly different versions of the necessary and sufficient condition discovered are equivalent. Next we consider
system (1) with all սi,= 0 together with system (2), and study the dual problem of transforming it to a linear observable system by a state and output coordinate change. Finally, we consider briefly system (l) and (2) with nonzero սi and study the problem of transforming it to a linear system that is both completely controllable and observable. Examples are given and applications to local stabilization and estimation are discussed. / Science, Faculty of / Mathematics, Department of / Graduate
| Identifer | oai:union.ndltd.org:UBC/oai:circle.library.ubc.ca:2429/26652 |
| Date | January 1987 |
| Creators | Tse, Wilfred See Foon |
| Publisher | University of British Columbia |
| Source Sets | University of British Columbia |
| Language | English |
| Detected Language | English |
| Type | Text, Thesis/Dissertation |
| Rights | For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use. |
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