Symbolic computation in nonlinear control systems analysis: The example of bilinearization

Mathematics and Computers in Simulation

Volumn 44, Issue 1, 1997, Pages 11-27

  Besançon, Gildas ^a   Bornard, Guy ^a  

^a GIPSA LAB   (France)

Author keywords

Bilinearization; Mathematica; Nonlinear systems; Observability; Symbolic computation

Indexed keywords

COMPUTATIONAL METHODS; CONTROL SYSTEM ANALYSIS; LINEARIZATION; THEOREM PROVING;

BILINEARIZATION; SOFTWARE PACKAGE MATHEMATICA; SYMBOLIC COMPUTATION;

NONLINEAR CONTROL SYSTEMS;

EID: 0031141942     PISSN: 03784754     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0378-4754(97)00003-7     Document Type: Article

References (18)

1. G. Jacob and F. Lamnabhi-Lagarrigue (Eds.), Algebraic computing in control, Lecture Notes in Control and Information Sci., Vol. 165 (Springer Verlag, Berlin, 1991).
2. A. Isidori, Nonlinear Control Systems, 2nd edn. (Springer-Verlag, Berlin, 1989).
3. H. Nijmeijer and A. Van der Schaft, Nonlinear Dynamical Control Systems (Springer, Berlin, 1990).
4. H. Van Essen and B. de Jager, Analysis and design of nonlinear control systems with the symbolic computation system maple in Proc. 2nd ECC, Groningen (1993) 2081-2085.
5. S. Wolfram, Mathematica, A System for Doing Mathematics by Computer (Addison-Wesley Publishing Company, 1988).
6. T. Othani and M. Masubuchi, A CAD system for nonlinear dynamic compensators using Mathematica, in Proc. 2nd IFAC Workshop on Syst. Struct, and Cont. Prague (1992) 364-367.
7. G. Besançon, Utilisation du calcul formel pour l'etude des systèmes non linéaires, Master's thesis, Institut National Polytechnique de Grenoble, Laboratoire d'Automatique de Grenoble, 1993.
8. H. Hammouri and J.P. Gauthier, Bilinearization up to output injection, Systems and Control Letters, Vol. 11 (1988) 139-149.
9. G. Besançon and G. Bornard, Performances and limitations of symbolic computation in nonlinear analysis and control: An example using mathematica, in Proc. IFAC Conf. on System Struct. and Control (Nantes, France, 1995) 617-622.
10. B. de Jager, The use of symbolic computation in nonlinear control: Is it viable?, IEEE Trans. on Automatic Control 40 (1995) 84-89.
11. A. Krener and A. Isidori, Linearization by output injection and nonlinear observers, Systems and Control Letters 3 (1983) 47-52.
12. J. Birk and M. Zeitz, Computer-aided analysis of nonlinear observation problems, in IFAC Proc., Nonlinear Control Systems Design Symposium (Bordeaux, France, June 1992) 251-256.
13. G. Besançon and G. Bornard, Symbolic computation aided design of observers for a class of nonlinear control systems, in Proc. American Control Conference (Seattle, WA, 1995), 3017-3018.
14. W.M. Boothby, An Introduction to Differentiable Manifolds and Riemannian Geometry (Academic Press, New York, 1975).
15. R. Hermann and A.J. Krener, Nonlinear controllability and observability, IEEE Trans. on Automatic Control 22 (1977) 728-740.
16. G. Besançon, Results on bilinearizability of nonlinear systems, Technic. Rep. 94067, LAG, 1994.
17. H. Hammouri and J.P. Gauthier, Global time-varying linearization up to output injection, Siam Journal on Control and Optimization 30 (1992) 1295-1310.
18. G. Besançon and G. Bornard, A condition for cascade time-varying linearization, in IFAC Proc., Nonlinear Control Systems Design Symposium (Tahoe City, CA, 1995) 684-689.