Abstract
Summary. Up to what extent is it possible to simplify the nonlinearities of a given discrete-time system through transformations involving feedbacks or outputinjections? Solutions to these problems, at the basis of several control and state estimation design procedures, take advantage of a combined use of geometric and algebraic methods, two major setups in nonlinear control theory strongly influenced by the fundamental work of Alberto Isidori. Links between these frameworks are illustrated in the present paper which is written to celebrate his 65th birthday.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
J.P. Barbot, S. Monaco, and D. Normand-Cyrot. Quadratic forms and approximated feedback linearization in discrete time. Int. J. of Control, 67:567–586, 1997.
I. Belmouhoud, M. Djemai, and J.P. Barbot. Observability quadratic normal form for discrete-time systems. IEEE Trans. on Automat. Contr., 50(7):1031–1037, 2005.
C. Califano, S. Monaco, and D. Normand-Cyrot. On the observer design in discrete time nonlinear systems. Systems & Control Letters, 49:255–265, 2003.
J.W. Grizzle. Feedback Linearization of Discrete-Time Systems, volume 83 of Lecture Notes in Control and Info. Sciences. Springer Verlag, Berlin, 1986.
B. Hamzi, J.P. Barbot, S. Monaco, and D. Normand-Cyrot. Nonlinear discrete-time control of systems with a Naimark-Sacker bifurcation. Systems & Control Letters, 44:245–258, 2001.
B. Hamzi, A.J. Krener, and W. Kang. The controlled center dynamics of discrete-time control bifurcations. Systems & Control Letters, 55:585–596, 2006.
B. Hamzi and I.A. Tall. Normal forms for nonlinear discrete-time control systems. Proc. of the 42nd IEEE Conf. on Decision and Contr., pages 1357–1361, 2003.
A. Isidori. Nonlinear Control Sytems. Springer Verlag, New York, 3rd edition, 1995.
W. Kang. Extended controller form and invariants of nonlinear control systems with a single input. Journal of Math. Syst. Estimation and Control, 6:27–51, 1996.
W. Kang and A.J. Krener. Extended quadratic controller normal form and dynamic state feedback linearization of nonlinear systems. SIAM J. Contr. Optimization, 30:1319–1337, 1992.
N. Kazantzis and C. Kravaris. Discrete-time nonlinear observer design using functional equations. Systems & Control Letters, 42:81–94, 2001.
A.J. Krener. Approximate linearization by state feedback and coordinate change. Systems & Control Letters, 5:181–185, 1984.
A.J. Krener and A. Isidori. Linearization by output-injection and nonlinear observers. Systems & Control Letters, 3:47–52, 1983.
A.J. Krener and L. Li. Normal forms and bifurcations of discrete-time nonlinear control systems. SIAM J. Contr. Optimization, 40:1697–1723, 2002.
S. Monaco and D. Normand-Cyrot. A unifying representation for nonlinear discrete-time and sampled dynamics. Journal of Math. Syst. Estimation and Control, 5(1):103–105, 1995.
S. Monaco and D. Normand-Cyrot. Nonlinear discrete-time representations, a new paradigm. Perspectives in Control, a tribute to Ioan DoréLandau, pages 191–205. Springer Verlag, London, 3rd edition, 1998.
S. Monaco and D. Normand-Cyrot. Normal forms and approximated feedback linearization in discrete time. Systems & Control Letters, 55:71–80, 2006.
I.A. Tall and W. Respondek. Feedback classification of nonlinear single-input control systems with controllable linearization: normal forms, canonical forms and invariants. SIAM J. Contr. Optimization, 41:1498–1531, 2003.
X.H. Xia and W.B. Gao. Nonlinear observer design by observer error linearization. SIAM J. Contr. Optimization, 27:199–216, 1989.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Monaco, S., Normand-Cyrot, D. (2008). Controller and Observer Normal Forms in Discrete-Time. In: Astolfi, A., Marconi, L. (eds) Analysis and Design of Nonlinear Control Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74358-3_22
Download citation
DOI: https://doi.org/10.1007/978-3-540-74358-3_22
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74357-6
Online ISBN: 978-3-540-74358-3
eBook Packages: EngineeringEngineering (R0)