An algorithm for feedback linearization. (English) Zbl 0789.93036
Summary: Previous methods for exact linearization by feedback have relied on solving Frobenius systems of partial differential equations of dimensions equal to the Kronecker indices. We describe an algorithm whereby one may find the linearizing feedback for any controllable linearizable system having distinct Kronecker indices with \(p\)-controls by purely algebraic calculations and integration of at most \(p\) one-dimensional Frobenius systems. The paper concludes with a concrete example considered by L. R. Hunt, Renjeng Su and G. Meyer [Differential geometric control theory, Proc. Conf., Mich. Technol. Univ. 1982, Prog. Math. 27, 268-298 (1983; Zbl 0543.93026)].
Citations:
Zbl 0543.93026References:
[1] | Gardner, R., The Method of Equivalence and Applications (1989), SIAM-CBMS: SIAM-CBMS Philadelphia · Zbl 0694.53027 |
[2] | Gardner, R.; Wilkens, G.; Shadwick, W., Feedback equivalence and symmetries of Brunovský normal forms, (Proceedings of the AMS-SIAM-IMS Conference on Control Theory and Multi-Body Systems (1989), AMS: AMS Providence), AMS Contemporary Mathematics Series · Zbl 0696.93051 |
[3] | Hunt, L. R.; Su, R.; Meyer, G., Design for multi-input nonlinear systems, (Differential Geometric Control Theory (1983), Birkhäuser: Birkhäuser Boston) · Zbl 0543.93026 |
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