Generic uniform observability analysis for bilinear systems. (English) Zbl 1153.93330
Summary: We study the property of generic uniform observability for structured bilinear systems. More precisely, to check whether or not a structured bilinear system is generically uniformly observable, we provide a group of necessary conditions and a second group of sufficient ones. These conditions are expressed in quite simple graphic-terms. On one hand, all the given conditions are easy to check because they deal with finding paths in a digraph. On the other hand, the proposed method is based on a graph-theoretic approach and assumes only a knowledge of the system’s structure. This makes the suggested approach particularly well suited to study large scale systems or systems with unknown parameters, as may be the case during a conception stage.
References:
| [1] | Bornard, G., & Hammouri, H. (2002). A graph approach to uniform observability of linear multi output systems. In Proceedings of the 41st IEEE conference on decision and control; Bornard, G., & Hammouri, H. (2002). A graph approach to uniform observability of linear multi output systems. In Proceedings of the 41st IEEE conference on decision and control |
| [2] | Boukhobza, T.; Hamelin, F.; Martinez-Martinez, S., State and input observability for structured linear systems: A graph-theoretic approach, Automatica, 43, 7, 1204-1210 (2007) · Zbl 1123.93024 |
| [3] | Boukhobza, T.; Hamelin, F.; Sauter, D., Uniform observability analysis for structured bilinear systems: A graph-theoretic approach, European Journal of Control, 12, 5, 505-518 (2006) · Zbl 1293.93110 |
| [4] | Commault, C.; Dion, J.-M.; Hovelaque, V., A geometric approach for structured systems: Application to disturbance decoupling, Automatica, 33, 3, 403-409 (1997) · Zbl 0878.93015 |
| [5] | Dion, J.-M.; Commault, C.; van der Woude, J., Generic properties and control of linear structured systems: A survey, Automatica, 39, 7, 1125-1144 (2003) · Zbl 1023.93002 |
| [6] | Gauthier, J.-P.; Bornard, G., Observability for any \(u(t)\) of a class of nonlinear systems, IEEE Transactions on Automatic Control, 26, 4, 922-926 (1981) · Zbl 0553.93014 |
| [7] | Gauthier, J.-P.; Kupka, I. A.K., Observability and observers for nonlinear systems, SIAM Journal of Control and Optimization, 32, 4, 975-994 (1994) · Zbl 0802.93008 |
| [8] | Grasselli, O. M., & Isidori, A. (1977). Deterministic state reconstruction and reachability of bilinear processes. In Proceedings of IEEE joint automatic control conference; Grasselli, O. M., & Isidori, A. (1977). Deterministic state reconstruction and reachability of bilinear processes. In Proceedings of IEEE joint automatic control conference |
| [9] | Hermann, R.; Krener, A. J., Nonlinear controllability and observability, IEEE Transactions on Automatic Control, 22, 6, 728-740 (1977) · Zbl 0396.93015 |
| [10] | Hovelaque, V.; Commault, C.; Dion, J.-M., Analysis of linear structured systems using a primal-dual algorithm, System & Control Letters, 27, 2, 73-85 (1996) · Zbl 0875.93117 |
| [11] | Kou, S. R.; Elliot, D. L.; Tarn, T. J., Observability of nonlinear systems, Information and Control, 22, 89-99 (1996) · Zbl 0252.93009 |
| [12] | Lévine, J., A graph-theoretic approach to input output decoupling and linearization, (Fossard, A. J.; Normand-Cyrot, D., Nonlinear systems (1997), Chapman & Hall: Chapman & Hall London, UK), 77-91, (Chapter 3) · Zbl 1081.93504 |
| [13] | Martinez-Martinez, S., Mader, T., Boukhobza, T., & Hamelin, F. (2006). LISA: A linear structured system analysis program. In Proceedings of the German-French institute for automation and robotics annual meeting; Martinez-Martinez, S., Mader, T., Boukhobza, T., & Hamelin, F. (2006). LISA: A linear structured system analysis program. In Proceedings of the German-French institute for automation and robotics annual meeting |
| [14] | Micali, S., & Vazirani, V. V. (1980). An \(O ( | V^{1 / 2} E | )\)Proceedings of the 21st annual symposium on the foundations of computer science; Micali, S., & Vazirani, V. V. (1980). An \(O ( | V^{1 / 2} E | )\)Proceedings of the 21st annual symposium on the foundations of computer science |
| [15] | Mohler, R. R., Nonlinear systems: Application to bilinear systems (1991), Prentice-Hall: Prentice-Hall Englewood Cliffs, USA · Zbl 0789.93059 |
| [16] | Svaricek, F. (1993). A graph theoretic approach for the investigation of the observability of bilinear systems. In Proceedings of the 12th IFAC world congress; Svaricek, F. (1993). A graph theoretic approach for the investigation of the observability of bilinear systems. In Proceedings of the 12th IFAC world congress |
| [17] | Trentelman, H. L.; Stoorvogel, A. A.; Hautus, M., Control theory for linear systems (2001), Springer: Springer London, UK · Zbl 0963.93004 |
| [18] | 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 |
| [19] | 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
