Necessary and sufficient conditions for the linearisability of two-input systems by a two-dimensional endogenous dynamic feedback

References

• Fliess, M., Lévine, J., Martin, P., & Rouchon, P. (1992). Sur les systèmes non linéaires différentiellement plats. Comptes rendus de l'Académie des sciences. Série I, Mathématique, 315, 619–624.
   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
• Fossas, E., & Franch, J. (2000). Linearization by prolongations and quotient of modules, a case study: The vertical take off and landing aircraft. In Proceedings wses international conference on applied and theoretical mathematics (pp. 1961–1965).
   Google Scholar
• Gstöttner, C., Kolar, B., & Schöberl, M. (2020a). On the linearization of flat two-input systems by prolongations and applications to control design. IFAC-PapersOnLine, 53(2), 5479–5486. 21st IFAC World Congress. https://doi.org/10.1016/j.ifacol.2020.12.1553
   Google Scholar
• Gstöttner, C., Kolar, B., & Schöberl, M. (2020b). A structurally flat triangular form based on the extended chained form. International Journal of Control. https://doi.org/10.1080/00207179.2020.1841302
   Web of Science ®Google Scholar
• Gstöttner, C., Kolar, B., & Schöberl, M. (2021a). On a flat triangular form based on the extended chained form. IFAC-PapersOnLine, 54(9), 245–252. 24th International symposium on mathematical theory of networks and systems (MTNS). https://doi.org/10.1016/j.ifacol.2021.06.082
   Google Scholar
• Gstöttner, C., Kolar, B., & Schöberl, M. (2021b). A finite test for the linearizability of two-input systems by a two-dimensional endogenous dynamic feedback. arXiv:2011.06929 [math.DS]. ECC 2021.
   Google Scholar
• Jakubczyk, B., & Respondek, W. (1980). On linearization of control systems. Bulletin L'Académie Polonaise des Science, Série des Sciences Mathématiques, 28, 517–522.
   Google Scholar
• Kai, T. (2006). Extended chained forms and their application to nonholonomic kinematic systems with affine constraints: control of a coin on a rotating table. In Proceedings of the 45th IEEE conference on decision and control (pp. 6104–6109). https://doi.org/10.1109/CDC.2006.377186
   Google Scholar
• Kolar, B., Schöberl, M., & Schlacher, K. (2016). Properties of flat systems with regard to the parameterization of the system variables by the flat output. IFAC-PapersOnLine, 49(18), 814–819. 10th IFAC symposium on nonlinear control systems NOLCOS 2016. https://doi.org/10.1016/j.ifacol.2016.10.266
   Google Scholar
• Lévine, J. (2009). Analysis and control of nonlinear systems: a flatness-based approach. Springer.
   Google Scholar
• Li, S., Nicolau, F., & Respondek, W. (2016). Multi-input control-affine systems static feedback equivalent to a triangular form and their flatness. International Journal of Control, 89(1), 1–24. https://doi.org/10.1080/00207179.2015.1056232
   Web of Science ®Google Scholar
• Li, S., Xu, C., Su, H., & Chu, J. (2013). Characterization and flatness of the extended chained system. In Proceedings of the 32nd Chinese control conference (pp. 1047–1051). IEEE.
   Google Scholar
• Martin, P., Devasia, S., & Paden, B. (1996). A different look at output tracking: control of a vtol aircraft. Automatica, 32(1), 101–107. https://doi.org/10.1016/0005-1098(95)00099-2
   Web of Science ®Google Scholar
• Martin, P., & Rouchon, P. (1994). Feedback linearization and driftless systems. Mathematics of Control, Signals and Systems, 7(3), 235–254. https://doi.org/10.1007/BF01212271
   Web of Science ®Google Scholar
• Nicolau, F., & Respondek, W. (2016a, December). Flatness of two-input control-affine systems linearizable via a two-fold prolongation. In 2016 IEEE 55th conference on decision and control (CDC) (pp. 3862–3867). https://doi.org/10.1109/CDC.2016.7798852
   Google Scholar
• Nicolau, F., & Respondek, W. (2016b). Two-input control-affine systems linearizable via one-fold prolongation and their flatness. European Journal of Control, 28, 20–37. https://doi.org/10.1016/j.ejcon.2015.11.001
   Web of Science ®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
• Nicolau, F., & Respondek, W. (2020). Normal forms for flat two-input control systems linearizable via a two-fold prolongation. IFAC-PapersOnLine, 53(2), 5441–5446. 21st IFAC World Congress. https://doi.org/10.1016/j.ifacol.2020.12.1545
   Google Scholar
• Nijmeijer, H., & van der Schaft, A. (1990). Nonlinear dynamical control systems. Springer.
   Google Scholar
• Pomet, J. (1997). On dynamic feedback linearization of four-dimensional affine control systems with two inputs. ESAIM: Control, Optimisation and Calculus of Variations, 2(1997), 151–230. https://doi.org/10.1051/cocv:1997107
   Google Scholar
• Schlacher, K., & Schöberl, M. (2013). A jet space approach to check Pfaffian systems for flatness. In 52nd IEEE conference on decision and control (pp. 2576–2581). https://doi.org/10.1109/CDC.2013.6760270
   Google Scholar
• Schöberl, M., Rieger, K., & Schlacher, K. (2010). System parametrization using affine derivative systems. In Proceedings 19th international symposium on mathematical theory of networks and systems (MTNS) (pp. 1737–1743).
   Google Scholar
• Schöberl, M., & Schlacher, K. (2010). On parametrizations for a special class of nonlinear systems. IFAC Proceedings Volumes, 43(14), 1261–1266. 8th IFAC symposium on nonlinear control systems. https://doi.org/10.3182/20100901-3-IT-2016.00051
   Google Scholar
• Schöberl, M., & Schlacher, K. (2011). On calculating flat outputs for Pfaffian systems by a reduction procedure – demonstrated by means of the VTOL example. In 2011 9th IEEE international conference on control and automation (ICCA) (pp. 477–482). https://doi.org/10.1109/ICCA.2011.6137922
   Google Scholar
• Schöberl, M., & Schlacher, K. (2014). On an implicit triangular decomposition of nonlinear control systems that are 1-flat – a constructive approach. Automatica, 50(6), 1649–1655. https://doi.org/10.1016/j.automatica.2014.04.007
   Web of Science ®Google Scholar
• Schöberl, M., & Schlacher, K. (2015). On geometric properties of triangularizations for nonlinear control systems. In M. K. Camlibel, A. A. Julius, R. Pasumarthy, and J. M. Scherpen (Eds.), Mathematical control theory i (pp. 237–255). Springer International Publishing.
   Google Scholar