Abstract
We solve a long-standing problem on the elimination of the state in the state-space representation of a nonlinear system. For this, we employ techniques from differential algebra.
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References
Hans BLOMBERG & Raimo YLINEN 1983: Algebraic Theory for Multivariable Linear Systems Academic Press, London, 1983.
Giuseppe CONTE, Claude H. MOOG & Annamaria PERDON 1988: Un théorème sur la représentation entrée-sortie d'un système non linéaire, C.R. Acad. Sci. Paris, 307, Série I (1988), 363–366.
P.E. CROUCH & Françoise LAMNABHI-LAGARRIGUE 1988: State space realizations of nonlinear systems defined by input-output differential equations, Proc. 8th Internat. Conf. Analysis Optimiz. Systems, Antibes, 1988, A. Bensousan and J.L. Lions eds, Lect. Notes Control Inform. Sci., 111 (1988), 138–149, Springer-Verlag, Berlin.
Michel FLIESS 1989: Automatique et corps differentiels, Forum Math., 1, 1989.
S.T. GLAD 1988: Nonlinear state space and input output descriptions using differential polynomials, this volume.
A. GROTHENDIECK & J.A. DIEUDONNE 1971: Eléments de Géométrie Algébrique, I, Springer-Verlag, Berlin, Heidelberg, New York, 1971.
Nathan JACOBSON 1974: Basic Algebra, I, W.H. Freeman & Co, San Francisco, 1974.
Joseph Fels RITT 1950: Differential Algebra, Amer. Math. Soc., New York, 1950.
A.J. van der SCHAFT 1988: Transformations of nonlinear systems under external equivalence, this volume.
Abraham SEIDENBERG 1956a: Some remarks on Hilbert's Nullstellensatz, Arch. Math., Vol.7, 1956, 235–240.
Abraham SEIDENBERG 1956b: An elimination theory for differential algebra, Univ. California Publications in Math., (N.S.), 3, no 2, 1956, 31–65.
Alfred TARSKI 1951: A decision method for elementary algebra and geometry (prepared for publication with the assistance of J.C.C. McKinsey), University of California Press, Berkeley and Los Angeles 1951, also in Collected Papers, Vol. 3: 1945–1957, 297–367, S.R. Givant & R.N. McKenzie, eds. Birkhäuser Verlag, Basel, 1986.
Jan C. WILLEMS 1983: Input-output and state space representation of finite dimensional linear time invariant systems, Lin. Alg. and its Appl., 50 (1983), 581–608.
Jan C. WILLEMS 1986: From time series to linear system, Part I: Finite dimensional linear time invariant systems, Automatica, Vol. 22 (1986), 561–580.
Wen-Tsun WU 1985: A constructive theory of differential algebraic geometry based on works of J.F. RITT with particular applications to mechanical theorem-proving of differential geometries, Proc. Conf. Differential Geometry and Differential Equations, SHANGHAI, 1985, Lect. Notes in Math., 1255(1987), 173–189, Springer-Verlag, Berlin Heidelberg.
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Diop, S. (1989). A state elimination procedure for nonlinear systems. In: Descusse, J., Fliess, M., Isidori, A., Leborgne, D. (eds) New Trends in Nonlinear Control Theory. Lecture Notes in Control and Information Sciences, vol 122. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0043028
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DOI: https://doi.org/10.1007/BFb0043028
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