Abstract
In this paper sufficient conditions for the global structural approximate controllability of polynomial sampled data systems will be derived based on a graph theoretical approach. The results obtained are an extension of the results of [1] from linear systems to polynomial systems. In a first step the notions of polynomial sampled data systems, structural controllability, and bundle graphs of those systems will be introduced. After a definition of general conductance and storage elements of a bundle graph, a theorem will be proved that provides sufficient conditions for the global structural approximate controllability of polynomial systems for large values of the state varaibles in a next step. In a third step a procedure will be presented for deriving a bundle graph cactus hedge from a given bundle graph. In a last step the theorem of step two will be extended to the whole state space using the well known concept of the mapping degree of a function.
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References
H. Hahn, H.-J. Sommer: Structural Controllability of Linear Systems: A Pure Graph Theoretical Proof, This volume.
C.T. Lin: Structural Controllability, IEEE, Trans. AC-19,1974,201-208
D. Cox, J. Little, D. O'Shea: Ideals, Varietes and Algorithms, Springer Verlag, 1992
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© 1997 Springer-Verlag Berlin Heidelberg
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Sommer, H.J., Hahn, H. (1997). Global structural approximate controllability of polynomial nonlinear systems. In: Pichler, F., Moreno-Díaz, R. (eds) Computer Aided Systems Theory — EUROCAST'97. EUROCAST 1997. Lecture Notes in Computer Science, vol 1333. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0025042
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DOI: https://doi.org/10.1007/BFb0025042
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