Abstract
Here we investigate the problem of transforming a nonlinear system on the torusT n by using global feedback and global changes of coordinates into an invariant system (i.e., a control system\(\dot x = f(x) + \sum\nolimits_{i = 1}^m {g_i (x)u_i }\) of whichf andg i are (left and right) invariant vector fields whenT 2 is considered as a Lie group). We provide a complete answer whenn=2 and give a sufficient condition and necessary conditions in the more general case.
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Dayawansa, W., Elliott, D. & Martin, C. Feedback transformations on tori. Math. Systems Theory 22, 213–219 (1989). https://doi.org/10.1007/BF02088298
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DOI: https://doi.org/10.1007/BF02088298