On controllability and observability of implicit systems. (English) Zbl 0699.93003
Summary: We apply differential inclusion techniques to investigate controllability and observability of descriptor systems. In particular we derive an analogue of rank condition for singular systems and prove duality of controllability and observability by trajectories without jumps.
MSC:
| 93B05 | Controllability |
| 93B07 | Observability |
| 34A99 | General theory for ordinary differential equations |
| 93C05 | Linear systems in control theory |
| 93C15 | Control/observation systems governed by ordinary differential equations |
References:
| [1] | Armentano, V. A., The pencil (sE−A) and controllability-observability for generalized linear systems: A geometric approach, (Proc. 23th CDC. Proc. 23th CDC, Las Vegas, NV (Dec. 1984 1984)), 1507-1510 |
| [2] | Aubin, J.-P.; Cellina, A., Differential Inclusions, (Grundlehren der Math. Wissenschaften, Vol. 264 (1984), Springer-Verlag: Springer-Verlag Berlin) · Zbl 0538.34007 |
| [3] | Aubin, J.-P.; Ekeland, I., (Applied Nonlinear Analysis (1984), Wiley-Interscience: Wiley-Interscience New York) · Zbl 0641.47066 |
| [4] | Aubin, J.-P.; Frankowska, H., Set-Valued Analysis, (Systems and Control, Foundations and Applications, Vol. 2 (1990), Birkhäuser: Birkhäuser Basel-Boston) · Zbl 0713.49021 |
| [5] | Aubin, J.-P.; Frankowska, H.; Olech, C., Controllability of convex processes, SIAM J. Control Optim., 24, 1192-1211 (1986) · Zbl 0607.49025 |
| [6] | Campbell, S. L., Singular Systems of Differential Equations (1980), Pitman: Pitman New York · Zbl 0419.34007 |
| [7] | Campbell, S. L., Singular Systems of Differential Equations II (1982), Pitman: Pitman New York · Zbl 0482.34008 |
| [8] | Cobb, D. J., On the solutions of linear differential equations with singular coefficients, J. Differential Equations, 46, 310-323 (1982) · Zbl 0489.34006 |
| [9] | Cobb, D. J., Controllability, observability and duality in singular systems, IEEE Trans. Automat. Control, 29, 1076-1082 (1984) |
| [10] | Filippov, A. F., Classical solutions of differential equations with multivalued right hand side, SIAM J. Control, 5, 609-621 (1967) · Zbl 0238.34010 |
| [11] | Frankowska, H., Set-valued analysis and some control problems, (Roxin, E., Modern Optimal Control. Modern Optimal Control, Proceedings of the International Conference 30 years of Modern Control Theory, Kingston (June 1988) (1989), Marcel Dekker: Marcel Dekker New York), 89-103 · Zbl 0702.49013 |
| [12] | Frankowska, H., Contingent cones to reachable sets of control systems, SIAM J. Control Optim., 27, 170-198 (1989) · Zbl 0671.49030 |
| [13] | Ozcaldiran, K., A geometric characterization of the reachable and the controllable subspaces of descriptor circuits, IEEE Trans. Circuits Systems Signal Process., 5, 37-48 (1986) · Zbl 0606.93017 |
| [14] | Ozcaldiran, K., Geometric notes on descriptor systems, (Proc. 26th CDC. Proc. 26th CDC, Los Angeles, CA (1986)), 1134-1137 |
| [15] | Yip, E. L.; Sincovec, R. F., Solvability, controllability and observability of continuous descriptor systems, IEEE Trans. Automat. Control, 26, 702-707 (1981) · Zbl 0482.93013 |
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