Abstract
The normal form is discussed for nonlinear systems affected by constant commensurate delays. Two different forms are argued. In particular, necessary and sufficient conditions are given under which a nonlinear time-delay system can be decomposed into a (weakly) observable subsystem and a non observable subsystem. Whenever such a decomposition exists, additional conditions are required to ensure the feedback linearization of the weakly observable subsystem. Finally, a full characterization is derived for the nonlinear time delay system to have an unobservable subsystem not directly affected by the input and a weakly observable subsystem which is linearizable by feedback. The performed analysis is carried out within a new geometric framework recently introduced in the literature.
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References
Califano, C., Marquez-Martinez, L., Moog, C.H.: Extended lie brackets for nonlinear time-delay systems. IEEE Trans. Autom. Control 56(9), 2213–2218 (2011)
Califano, C., Marquez-Martinez, L., Moog, C.H.: Linearization of time-delay systems by input-output injection and output transformation. Automatica 49(6), 1932–1940 (2013)
Califano, C., Monaco, S., Normand-Cyrot, D.: On the discrete-time normal form. IEEE Trans. Autom. Control 43(11), 1654–1658 (1998)
Califano, C., Moog, C.H.: De l’existence de la forme normale pour les systemes non lineaires a retards. In: Proceedings of Conference Internationale Francophone d’Automatique, pp. 37–42 (2012)
Califano, C., Moog, C.H.: Coordinates transformations in nonlinear time-delay systems. In: Proceedings of the 53rd IEEE Conference on Decision and Control, pp. 475–480 (2014)
Garate-Garcia, A., Marquez-Martinez, L., Cuesta-Garcia, J., Garcia-Ramirez, E.: A computer algebra system for analysis and control of nonlinear time-delay systems. Adv. Eng. Softw. 65, 138–148 (2013)
Germani, A., Manes, C., Pepe, P.: Linearization of input-output mapping for nonlinear delay systems via static state feedback. In: Proceedings of the IEEE-IMACS Conference on Computer Engineering in System Applications, pp. 599–602 (1996)
Germani, A., Manes, C., Pepe, P.: Input-output linearization with delay cancellation for nonlinear delay systems: the problem of the internal stability. Int. J. Robust Nonlinear Control 13(9), 909–937 (2003)
Gu, K., Kharitonov, V., Chen, J.: Stability of Time-Delay Systems. Birkhauser, Boston (2003)
Isidori, A.: Nonlinear Control Systems, 3rd edn. Springer, New York (1995)
Marquez-Martinez, L., Moog, C.H., Velasco-Villa, M.: Observability and observers for nonlinear systems with time delay. Kybernetika 38(4), 445–456 (2002)
Michiels, W., Niculescu, S-I.: Stability and Stabilization of Time-Delay Systems. An Eigen-value-Based Approach. SIAM, Philadelphia (2007). (Advances in Design and Control, 12 )
Oguchi, T.: A finite spectrum assignment for retarded non-linear systems and its solvability condition. Int. J. Control 80(6), 898–907 (2007)
Pepe, P., Jiang, Z.-P.: A Lyapunov Krasovskii methodology for ISS and iISS of time-delay systems. Syst. Control Lett. 55(12), 1006–1014 (2006)
Xia, X., Marquez-Martinez, L., Zagalak, P., Moog, C.H.: Analysis of nonlinear time-delay systems using modules over non-commutative rings. Automatica 38(9), 1549–1555 (2002)
Zheng, G., Barbot, J., Boutat, D.: Identification of the delay parameter for nonlinear time-delay systems with unknown inputs. Automatica 49(6), 1755–1760 (2013)
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Califano, C., Moog, C.H. (2016). On the Existence of the Normal Form for Nonlinear Delay Systems. In: Karafyllis, I., Malisoff, M., Mazenc, F., Pepe, P. (eds) Recent Results on Nonlinear Delay Control Systems. Advances in Delays and Dynamics, vol 4. Springer, Cham. https://doi.org/10.1007/978-3-319-18072-4_6
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DOI: https://doi.org/10.1007/978-3-319-18072-4_6
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