On the exact linearisation and control of flat discrete-time systems

References

• Aranda-Bricaire, E., & Kotta, Ü. (2001). Generalized controlled invariance for discrete-time nonlinear systems with an application to the dynamic disturbance decoupling problem. IEEE Transactions on Automatic Control, 46(1), 165–171. https://doi.org/10.1109/9.898712
   Web of Science ®Google Scholar
• Aranda-Bricaire, E., & Moog, C. (2008). Linearization of discrete-time systems by exogenous dynamic feedback. Automatica, 44(7), 1707–1717. https://doi.org/10.1016/j.automatica.2007.10.030
   Web of Science ®Google Scholar
• Delaleau, E., & Rudolph, J. (1998). Control of flat systems by quasi-static feedback of generalized states. International Journal of Control, 71(5), 745–765. https://doi.org/10.1080/002071798221551
   Web of Science ®Google Scholar
• Diwold, J., Kolar, B., & Schöberl, M. (2022a). Discrete-time flatness-based control of a gantry crane. Control Engineering Practice, 119, Article ID 104980. https://doi.org/10.1016/j.conengprac.2021.104980
   Web of Science ®Google Scholar
• Diwold, J., Kolar, B., & Schöberl, M. (2022b). A trajectory-based approach to discrete-time flatness. IEEE Control Systems Letters, 6, 289–294. https://doi.org/10.1109/LCSYS.2021.3071177
   Google Scholar
• Fliess, M., Lévine, J., Martin, P., & Rouchon, P. (1995). Flatness and defect of non-linear systems: Introductory theory and examples. International Journal of Control, 61(6), 1327–1361. https://doi.org/10.1080/00207179508921959
   Web of Science ®Google Scholar
• Fliess, M., Lévine, J., Martin, P., & Rouchon, P. (1999). A Lie–Bäcklund approach to equivalence and flatness of nonlinear systems. IEEE Transactions on Automatic Control, 44(5), 922–937. https://doi.org/10.1109/9.763209
   Web of Science ®Google Scholar
• Grizzle, J. (1986). Feedback linearization of discrete-time systems. In A. Bensoussan & J. Lions (Eds.), Analysis and optimization of systems (Vol. 83, pp. 273–281). Springer.
   Google Scholar
• Gstöttner, C., Kolar, B., & Schöberl, M. (2021a). Control of (x,u)-flat systems by quasi-static feedback of classical states. arXiv e-prints. arXiv:2110.12995 [math.OC].
   Google Scholar
• Gstöttner, C., Kolar, B., & Schöberl, M. (2021b). Necessary and sufficient conditions for the linearisability of two-input systems by a two-dimensional endogenous dynamic feedback. International Journal of Control. https://doi.org/10.1080/00207179.2021.2015542
   Web of Science ®Google Scholar
• Guillot, P., & Millérioux, G. (2020). Flatness and submersivity of discrete-time dynamical systems. IEEE Control Systems Letters, 4(2), 337–342. https://doi.org/10.1109/LCSYS.7782633
   Google Scholar
• Kaldmäe, A. (2021). Algebraic necessary and sufficient condition for difference flatness. International Journal of Control. https://doi.org/10.1080/00207179.2021.1908598
   Web of Science ®Google Scholar
• Kaldmäe, A., & Kotta, Ü. (2013). On flatness of discrete-time nonlinear systems. In Proceedings 9th IFAC symposium on nonlinear control systems (pp. 588–593).
   Google Scholar
• Kiefer, T., Kugi, A., & Kemmetmüller, W. (2004). Modeling and flatness-based control of a 3 DOF helicopter laboratory experiment. In Proceedings 6th IFAC symposium on nonlinear control systems (pp. 207–212).
   Google Scholar
• Kolar, B., Diwold, J., & Schöberl, M. (2022). Necessary and sufficient conditions for difference flatness. IEEE Transactions on Automatic Control, https://doi.org/10.1109/TAC.2022.3151615
   Web of Science ®Google Scholar
• Kolar, B., Kaldmäe, A., Schöberl, M., Kotta, Ü., & Schlacher, K. (2016). Construction of flat outputs of nonlinear discrete-time systems in a geometric and an algebraic framework. IFAC-PapersOnLine, 49(18), 796–801. https://doi.org/10.1016/j.ifacol.2016.10.263
   Google Scholar
• Kolar, B., Schöberl, M., & Diwold, J. (2021). Differential-geometric decomposition of flat nonlinear discrete-time systems. Automatica, 132, Article ID 109828. https://doi.org/10.1016/j.automatica.2021.109828
   Web of Science ®Google Scholar
• Kotta, Ü. (1990). Right inverse of a discrete time non-linear system. International Journal of Control, 51(1), 1–9. https://doi.org/10.1080/00207179008934047
   Web of Science ®Google Scholar
• Kotta, Ü. (1995). Inversion method in the discrete-time nonlinear control systems synthesis problems (Vol. 205). Springer.
   Google Scholar
• Kotta, Ü., & Nijmeijer, H. (1991). Dynamic disturbance decoupling for nonlinear discrete-time systems (in Russian). Proceedings of the Academy of Sciences of USSR Technical Cybernetics, 52–59.
   Google Scholar
• Nicolau, F., & Respondek, W. (2017). Flatness of multi-input control-affine systems linearizable via one-fold prolongation. SIAM Journal on Control and Optimization, 55(5), 3171–3203. https://doi.org/10.1137/140999463
   Web of Science ®Google Scholar
• Nicolau, F., & Respondek, W. (2019). Normal forms for multi-input flat systems of minimal differential weight. International Journal of Robust and Nonlinear Control, 29(10), 3139–3162. https://doi.org/10.1002/rnc.v29.10
   Web of Science ®Google Scholar
• Nijmeijer, H., & van der Schaft, A. (1990). Nonlinear dynamical control systems. Springer.
   Google Scholar
• Orosco-Guerrero, R., Velasco-Villa, M., & Aranda-Bricaire, E. (2004). Discrete-time controller for a wheeled mobile robot. In Proceedings XI congreso latinoamericano de control automatico.
   Google Scholar
• Rudolph, J. (2021). Flatness-based control: An introduction. Shaker Verlag.
   Google Scholar
• Sira-Ramirez, H., & Agrawal, S. (2004). Differentially flat systems. Marcel Dekker.
   Google Scholar
• Sira-Ramirez, H., & Rouchon, P. (2003). Exact delayed reconstructors in nonlinear discrete-time systems control. In A. Zinober & D. Owens (Eds), Nonlinear and adaptive control (Vol. 281, pp. 351–360). Springer.
   Google Scholar