, Ülle Kotta , Alexey Ye. Shumsky, Alexey N. ZhirabokThe connection between the concepts of the single-experiment and the multi-experiment unobservability of a nonlinear discrete-time control system is studied. The main result claims that if the system is single-experiment unobservable and the observable space is integrable, then the system is also multi-experiment unobservable. For the proof of the main result a novel mathematical technique, the so-called algebra of functions, is used.
1. Albertini, F. and D’Alessandro, D. Observability and forward–backward observability of discrete-time nonlinear systems. Math. Control Signals Syst., 2002, 15, 275–290.
doi:10.1007/s004980200011
2. Kotta, Ü. Decomposition of discrete-time nonlinear control systems. Proc. Estonian Acad. Sci. Phys. Math., 2005, 54, 154–161.
3. Kotta, Ü. and Schlacher, K. Possible non-integrability of observable space for discrete-time nonlinear control systems. In Proceedings of the 17th World Congress of the International Federation of Automatic Control, Seoul, Korea, July 6–11, 2008 (Chung, M. J., Misra, P., and Shim, H., eds). Seoul, 2008, 9852–9856.
4. Shumsky, A. Ye. and Zhirabok, A. N. Nonlinear diagnostic filter design: algebraic and geometric points of view. Int. J. Appl. Math. Comput. Sci., 2006, 16, 115–127.
5. Wang, Y. and Sontag, E. D. Orders of input/output differential equations and state-space dimensions. SIAM J. Control Optim., 1995, 33, 1102–1126.
doi:10.1137/S0363012993246828
6. Zhirabok, A. Observability and controllability properties of nonlinear dynamic systems. J. Comput. Syst. Sci. Int., 1998, 37, 1–4.
7. Zhirabok, A. Canonical decomposition of nonlinear dynamic systems based on invariant functions. Autom. Remote Control, 2006, 67, 3–15.
doi:10.1134/S0005117906040011
8. Zhirabok, A. N. and Shumsky, A. Ye. The Algebraic Methods for Analysis of Nonlinear Dynamic System. Dalnauka, Vladivostok, 2008 (in Russian).
