Observability analysis for structured bilinear systems: a graph-theoretic approach. (English) Zbl 1129.93331

Summary: This paper is devoted to the generic observability analysis for structured bilinear systems using a graph-theoretic approach. On the basis of a digraph representation, we express in graphic terms the necessary and sufficient conditions for the generic observability of structured bilinear systems. These conditions have an intuitive interpretation and are easy to check by hand for small systems and by means of well-known combinatorial techniques for large-scale systems.


93B07 Observability
93B18 Linearizations
93B25 Algebraic methods
93C10 Nonlinear systems in control theory
05C20 Directed graphs (digraphs), tournaments
Full Text: DOI HAL


[1] Andrë, N., Sparse systems, digraph approach of large-scale linear systems theory (1985), TÜV: TÜV Köln, Germany
[4] D’Angelo, H., Linear time varying systems: Analysis and synthesis (1970), Allyn & Bacon: Allyn & Bacon Boston, USA · Zbl 0202.08502
[5] Davison, E. J.; Wang, S. H., Properties of linear time-invariant multivariable systems subject to arbitrary output and state feedback, IEEE Transactions on Automatic Control, AC-18, 1, 24-32 (1973) · Zbl 0262.93018
[6] Dion, J.-M.; Commault, C.; van der Woude, J. W., Generic properties and control of linear structured systems: a survey, Automatica, 39, 7, 1125-1144 (2003) · Zbl 1023.93002
[8] Kailath, T., Linear systems. Prentice Hall Information and system science series (1980), Prentice-Hall: Prentice-Hall Englewood Cliffs
[12] Murota, K., System analysis by graphs and matroids (1987), Springer: Springer New York, USA
[13] Reinschke, K. J., Multivariable control. A graph theoretic approach (1988), Springer: Springer New York, USA · Zbl 0682.93006
[14] Sen, P., On the choice of input for observability in bilinear systems, IEEE Transactions on Automatic Control, AC-26, 2, 451-454 (1981) · Zbl 0472.93017
[16] van der Woude, J. W., A graph theoretic characterization for the rank of the transfer matrix of a structured system, Mathematics of Control, Signals and Systems, 4, 1, 33-40 (1991) · Zbl 0747.93030
[17] van der Woude, J. W., The generic number of invariant zeros of a structured linear system, SIAM Journal of Control and Optimization, 38, 1, 1-21 (2000) · Zbl 0952.93056
[18] Williamson, D., Observation of bilinear systems with application to biological control, Automatica, 13, 3, 243-254 (1977) · Zbl 0351.93008
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.