Previous article On the Genericity of the Observability of Uncontrolled Discrete Nonlinear SystemsJ. C. VivaldaJ. C. Vivaldahttps://doi.org/10.1137/S0363012902403997PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractIn this paper, it is proven that, generically, a nonlinear discrete system given on a compact manifold X is observable.[1] Ralph Abraham and , Joel Robbin, Transversal mappings and flows, An appendix by Al Kelley, W. A. Benjamin, Inc., New York‐Amsterdam, 1967x+161 39:2181 Google Scholar[2] Dirk Aeyels, Generic observability of differentiable systems, SIAM J. Control Optim., 19 (1981), 595–603 83f:58044 LinkISIGoogle Scholar[3] Dirk Aeyels, On the number of samples necessary to achieve observability, Systems Control Lett., 1 (1981/82), 92–94 83i:93007 CrossrefISIGoogle Scholar[4] Google Scholar[5] J. Gauthier and , I. Kupka, Observability for systems with more outputs than inputs and asymptotic observers, Math. Z., 223 (1996), 47–78 97i:93022 CrossrefISIGoogle Scholar[6] M. Golubitsky and , V. Guillemin, Stable mappings and their singularities, Springer‐Verlag, 1973x+209, Graduate Texts in Mathematics, Vol. 14 49:6269 CrossrefGoogle Scholar[7] J. Stark, Delay embeddings for forced systems. I. Deterministic forcing, J. Nonlinear Sci., 9 (1999), 255–332 10.1007/s003329900072 2000e:37020 CrossrefISIGoogle Scholar[8] Floris Takens, Detecting strange attractors in turbulence, Lecture Notes in Math., Vol. 898, Springer, Berlin, 1981, 366–381 83i:58065 Google Scholar[9] Hassler Whitney, Elementary structure of real algebraic varieties, Ann. of Math. (2), 66 (1957), 545–556 20:2342 CrossrefISIGoogle ScholarKeywordsobservabilitydiscrete-time systemstransversality Previous article FiguresRelatedReferencesCited ByDetails Strong Differential Observability for Sampled-Time SystemsSabeur Ammar, Jean-Claude Vivalda, and Basma ZitouniSIAM Journal on Control and Optimization, Vol. 58, No. 6 | 17 December 2020AbstractPDF (535 KB)Genericity of the Strong Observability for Sampled SystemsSabeur Ammar, Majid Massaoud, and Jean-Claude VivaldaSIAM Journal on Control and Optimization, Vol. 56, No. 2 | 17 April 2018AbstractPDF (544 KB)On the stability of a differential Riccati equation for continuous-discrete observersInternational Journal of Control, Vol. 89, No. 2 | 28 August 2015 Cross Ref Direct Filtering: A New Approach to Optimal Filter Design for Nonlinear SystemsIEEE Transactions on Automatic Control, Vol. 58, No. 1 | 1 Jan 2013 Cross Ref The filter design from data (FD2) problem: parametric-statistical approachInternational Journal of Robust and Nonlinear Control, Vol. 22, No. 16 | 13 September 2011 Cross Ref High-Speed Piecewise Affine Virtual SensorsIEEE Transactions on Industrial Electronics, Vol. 59, No. 2 | 1 Feb 2012 Cross Ref A new approach to optimal filter design for nonlinear systemsProceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference | 1 Dec 2009 Cross Ref Impulsive Control of Discrete Systems With Time DelayIEEE Transactions on Automatic Control, Vol. 54, No. 4 | 1 Apr 2009 Cross Ref On the genericity of the differential observability of controlled discrete-time systems2008 47th IEEE Conference on Decision and Control | 1 Jan 2008 Cross Ref On the Genericity of the Differential Observability of Controlled Discrete-Time SystemsSabeur Ammar, Mohamed Mabrouk, and Jean-Claude VivaldaSIAM Journal on Control and Optimization, Vol. 46, No. 6 | 21 December 2007AbstractPDF (236 KB)Filter design from data: direct vs. two-step approaches2006 American Control Conference | 1 Jan 2006 Cross Ref NONLINEAR VIRTUAL SENSORS DESIGN FROM DATAIFAC Proceedings Volumes, Vol. 39, No. 1 | 1 Jan 2006 Cross Ref On the genericity of the observability of controlled discrete-time systemsESAIM: Control, Optimisation and Calculus of Variations, Vol. 11, No. 2 | 15 March 2005 Cross Ref Volume 42, Issue 4| 2003SIAM Journal on Control and Optimization1143-1522 History Published online:26 July 2006 InformationCopyright © 2003 Society for Industrial and Applied MathematicsKeywordsobservabilitydiscrete-time systemstransversalityMSC codes57R4093B0793B2793C55PDF Download Article & Publication DataArticle DOI:10.1137/S0363012902403997Article page range:pp. 1509-1522ISSN (print):0363-0129ISSN (online):1095-7138Publisher:Society for Industrial and Applied Mathematics