**Page description appears here**

“A new perspective on stable inversion of non-minimum phase nonlinear systems”

Authors: Alexey Pavlov and Kristin Y. Pettersen,
Affiliation: NTNU, Department of Engineering Cybernetics
Reference: 2008, Vol 29, No 1, pp. 29-35.

     Valid XHTML 1.0 Strict

Keywords: Stable inversion, non-minimum phase systems, nonlinear systems, convergent systems

Abstract: We present a new perspective on the problem of stable inversion of nonlinear non-minimum phase systems. It is based on the notion of convergent systems. The machinery of convergent systems allows us to obtain novel qualitative and quantitative conditions for solving this problem. These conditions provide insight into the dynamics behind the stable inversion problem and make it possible to treat this problem in a non-local way. Qualitatively, they cover the conditions for the stable inversion of non-minimum phase nonlinear systems previously reported in literature and allow us to solve this problem for a broader class of systems. The proposed approach is supported with a novel computational method.

PDF PDF (148 Kb)        DOI: 10.4173/mic.2008.1.3

DOI forward links to this article:
  [1] Alexey Pavlov and Kristin Y. Pettersen (2007), doi:10.1109/CDC.2007.4434276
  [2] H. T. van der Scheer and A. Doelman (2017), doi:10.1007/s00422-017-0722-1
  [3] Jurgen van Zundert and Tom Oomen (2017), doi:10.1080/00207179.2017.1380315

[1] Demidovich, B. (1967). Lectures on stability theory, in Russian. Nauka, Moscow.
[2] Devasia, S. (1999). Approximated stable inversion for nonlinear systems with nonhyperbolic internal dynamics, IEEE Trans. Automatic Control, 44:1419-1424 doi:10.1109/9.774114
[3] Devasia, S., Chen, D., Paden, B. (1996). Nonlinear inversion-based output tracking, IEEE Trans. Automatic Control. 41:930-942 doi:10.1109/9.508898
[4] Devasia, S. Paden, B. (1998). Stable inversion for nonlinear nonminimum-phase time-varying systems, IEEE Trans. Automatic Control, 43:283-288 doi:10.1109/9.661082
[5] Hunt, L., Ramakrishna, V., Meyer, G. (1998). Stable inversion and parameter variations, Systems and Control Letters, 34:203-207 doi:10.1016/S0167-6911(98)00026-7
[6] Hunt, L. R. Meyer, G. (1997). Stable inversion for nonlinear systems, Automatica, 33:1549-1554 doi:10.1016/S0005-1098(97)00064-2
[7] Isidori, A. (1995). Nonlinear control systems, 3rd ed, Springer-Verlag, London.
[8] Khalil, H. (2002). Nonlinear systems, 3rd ed, Prentice Hall, Upper Saddle River.
[9] Kreyszig, E. (1978). Introductory Functional Analysis with Applications, John Wiley and Sons, New York.
[10] Parker, T. Chua, L. (1989). Practical numerical algorithms for chaotic systems, Springer-Verlag, New York.
[11] Pavlov, A., Pogromsky, A., van de Wouw, N., Nijmeijer, H. (2004). Convergent dynamics, a tribute to Boris Pavlovich Demidovich, Systems and Control Letters. 52:257-261 doi:10.1016/j.sysconle.2004.02.003
[12] Pavlov, A., van de Wouw, N., Nijmeijer, H. (2002). Convergent systems and the output regulation problem, In Proc. of IEEE Conf. Decision and Control. pp. 2681-2686.
[13] Pavlov, A., van de Wouw, N., Nijmeijer, H. (2005). Convergent systems: analysis and design, In Control and Observer Design for Nonlinear Finite and Infinite Dimensional Systems, pp. 131-146. Springer doi:10.1007/11529798_9
[14] Pavlov, A., van de Wouw, N., Nijmeijer, H. (2005). Uniform output regulation of nonlinear systems: a convergent dynamics approach, Birkhäuser, Boston.
[15] Zeng, G. Hunt, L. (2000). Stable inversion of nonlinear discrete-time systems, IEEE Trans. Automatic Control. 45:1216-1220 doi:10.1109/9.863610

  title={{A new perspective on stable inversion of non-minimum phase nonlinear systems}},
  author={Pavlov, Alexey and Pettersen, Kristin Y.},
  journal={Modeling, Identification and Control},
  publisher={Norwegian Society of Automatic Control}


Oct 2018: MIC reaches 3000 DOI Forward Links. The last 1000 took 2 years and 5 months.

May 2016: MIC reaches 2000 DOI Forward Links. The first 1000 took 34 years, the next 1000 took 2.5 years.

July 2015: MIC's new impact factor is now 0.778. The number of papers published in 2014 was 21 compared to 15 in 2013, which partially explains the small decrease in impact factor.

Aug 2014: For the 3rd year in a row MIC's impact factor increases. It is now 0.826.

Dec 2013: New database-driven web-design enabling extended statistics. Article number 500 is published and MIC reaches 1000 DOI Forward Links.

Jan 2012: Follow MIC on your smartphone by using the RSS feed.


July 2011: MIC passes 1000 ISI Web of Science citations.

Mar 2010: MIC is now indexed by DOAJ and has received the Sparc Seal seal for open access journals.

Dec 2009: A MIC group is created at LinkedIn and Twitter.

Oct 2009: MIC is now fully updated in ISI Web of Knowledge.