Krener, Arthur J. Approximate linearization by state feedback and coordinate change. (English) Zbl 0555.93027 Syst. Control Lett. 5, 181-185 (1984). Necessary and sufficient conditions in terms of Lie brackets are derived for the existence of transformations \(x=x(\xi)\), \(u=\alpha (\xi)+\beta (\xi)\mu\) which transform the system \({\dot \xi}=g^ 0(\xi)+g(\xi)\mu\) to the system \(\dot x=Ax+Bu+O(\xi,\mu)^{p+1}\). Reviewer: P.Brunovsky Cited in 38 Documents MSC: 93C10 Nonlinear systems in control theory 93B17 Transformations 17B05 Structure theory for Lie algebras and superalgebras Keywords:linearization; Lie brackets; transformations PDFBibTeX XMLCite \textit{A. J. Krener}, Syst. Control Lett. 5, 181--185 (1984; Zbl 0555.93027) Full Text: DOI References: [1] Brockett, R. W., Feedback invariants for nonlinear systems, (Proceedings, IFAC Congress. Proceedings, IFAC Congress, Helsinki (1978)) · Zbl 0457.93028 [2] Freund, E., Fast nonlinear control with arbitrary pole-placement for industrial robots and manipulators, (Bradley; etal., Robot Motion (1982), MIT Press: MIT Press Berlin-New York), 147-167 [3] Hunt, L. R.; Su, R., Linear equivalents of nonlinear time varying systems, (Proceedings MTNS Symposium. Proceedings MTNS Symposium, Santa Monica (1981)), 119-123 [4] Jakubczyk, B.; Respondek, W., On the linearization of control systems, Bull. Acad. Polon. Sci. Ser. Math. Astron. Physics, 28, 517-522 (1980) · Zbl 0489.93023 [5] Krener, A. J., On the equivalence of control systems and the linearization of nonlinear systems, SIAM J. Control, 11, 670-676 (1973) · Zbl 0243.93009 [6] Krener, A. J., New approaches to the design of nonlinear compensators, (Proceedings of Berkeley Ames Conf. on Non-linear Problems. Proceedings of Berkeley Ames Conf. on Non-linear Problems, Aerodynamics and Flight Control (1984), Math. Sci. Press) · Zbl 0916.93019 [7] Meyer, G.; Cicolani, L., A formal structure for advanced automatic flight control systems, NASA TN D-7940 (1975) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.