Balanced realizations near stable invariant manifolds

Automatica

Volumn 42, Issue 4, 2006, Pages 653-659

  Gray, W Steven ^a,b  

^a Old Dominion University   (United States)

^b OLD DOMINION UNIVERSITY   (United States)

Author keywords

Balanced realizations; Invariant manifolds; Nonlinear systems

Indexed keywords

BALANCED REALIZATIONS; INVARIANT MANIFOLDS;

AUTOMATION;

NONLINEAR SYSTEMS;

EID: 33244466080     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.automatica.2005.12.007     Document Type: Article

References (18)

1. W.M. Boothby An introduction to differentiable manifolds and Riemannian geometry 1975 Academic Press Orlando, FL
2. J. Guckenheimer, and P. Holmes Nonlinear oscillations, dynamical systems, and bifurcations of vector fields 1983 Springer New York
3. T. Kato Perturbation theory for linear operators (2nd ed.) 1976 Springer Heidelberg
4. E.B. Lee, and L. Markus Foundations of optimal control theory 1967 Wiley New York
5. D.G. Meyer Fractional balanced reduction - model reduction via a fractional representation IEEE Transactions on Automatic Control 35 12 1990 1341 1345
6. B.C. Moore Principal component analysis in linear systems: Controllability, observability, and model reduction IEEE Transactions on Automatic Control 26 1 1981 17 32
7. R. Ober, and D. McFarlane Balanced canonical forms for minimal systems: A normalized coprime factor approach Linear Algebra and Its Applications 122-124 1989 23 64
8. T. Poston, and I.N. Stewart Catastrophe theory and its applications 1978 Pitman Publishing London
9. M.G. Safonov, R.Y. Chiang, and D.J.N. Limebeer Optimal Hankel model reduction for nonminimal systems IEEE Transactions on Automatic Control 35 4 1990 496 502
10. J.M.A. Scherpen Balancing for nonlinear systems Systems & Control Letters 21 2 1993 143 153
11. Scherpen, J.M.A. (1994). Balancing for nonlinear systems. Doctoral dissertation, University of Twente, The Netherlands.
12. J.M.A. Scherpen, and W.S. Gray Minimality and local state decompositions of a nonlinear state space realization using energy functions IEEE Transactions on Automatic Control 45 11 2000 2079 2086
13. Varga, A. (1997). Solution of positive periodic discrete Lyapunov equations with applications to the balancing of periodic systems. Proceedings of the 1997 European control conference, Brussels, Belgium.
14. Verriest, E. I., & Gray, W. S. (2000). Flow balancing nonlinear systems. Proceedings of the 2000 international symposium on mathematical theory of networks and systems, Perpignan, France.
15. Verriest, E. I., & Gray, W. S. (2001a). Discrete-time nonlinear balancing. The fifth IFAC nonlinear control systems design symposium (pp. 515-520), Saint Petersburg, Russia.
16. Verriest, E. I., & Gray, W. S. (2001b). Nonlinear balanced realizations. Proceedings of the 40th IEEE conference on decision and control (pp. 3250-3251), Orlando, FL.
17. Verriest, E. I., & Helmke, U. (1998). Periodic balanced realizations. The IFAC conference on structure and control (pp. 519-524). Nantes, France.
18. E.I. Verriest, and T. Kailath On generalized balanced realizations IEEE Transactions on Automatic Control 28 8 1983 833 844