On feedback equivalence of nonlinear systems. (English) Zbl 0537.93038
Summary: Conditions are derived under which a given system can be modified by means of feedback to obtain a new system whose output is influenced only by a linear and controllable dynamics.
MSC:
| 93C10 | Nonlinear systems in control theory |
| 93B50 | Synthesis problems |
| 58A30 | Vector distributions (subbundles of the tangent bundles) |
| 93B17 | Transformations |
| 37C80 | Symmetries, equivariant dynamical systems (MSC2010) |
References:
| [1] | Brockett, R. W., Feedback invariants for nonlinear systems, (Proc. VII IFAC Congress. Proc. VII IFAC Congress, Helsinki (1978)), 1115-1120 · Zbl 0457.93028 |
| [2] | Jakubczyk, B.; Respondek, W., On linearization of control systems, Bull. Acad. Polonaise Sci. Sér. Sci. Math., 28, 517-522 (1980) · Zbl 0489.93023 |
| [3] | Isidori, A.; Krener, A. J.; Gori-Giorgi, C.; Monaco, S., Nonlinear decoupling via feedback: a differential geometric approach, IEEE Trans. Aut. Control, 26, 331-345 (1981) · Zbl 0481.93037 |
| [4] | Hirschorn, R. M., (A, B) invariant distributions and the disturbance decoupling of nonlinear systems, SIAM J. Control Optim., 17, 1-19 (1981) · Zbl 0474.93036 |
| [5] | Nijmeijer, H., Controlled invariance for affine control systems, Int. J. Control, 34, 825-833 (1981) · Zbl 0467.49025 |
| [6] | Isidori, A.; Krener, A. J.; Gori-Giorgi, C.; Monaco, S., Locally (f, g) invariant distributions, Systems Control Lett., 1, 12-15 (1981) · Zbl 0483.93051 |
| [7] | H. Nijmeijer and A.J. van der Schaft, Controlled invariance for nonlinear control systems, to appear in IEEE Trans. Aut. Control.; H. Nijmeijer and A.J. van der Schaft, Controlled invariance for nonlinear control systems, to appear in IEEE Trans. Aut. Control. · Zbl 0492.93035 |
| [8] | Claude, D., Decoupling of nonlinear systems, Systems Control Lett., 1, 242-248 (1982) · Zbl 0473.93043 |
| [9] | Tsinias, J.; Kalouptsidis, N., Transforming a controllable multiinput nonlinear system to a single input controllable system by feedback, Systems Control Lett., 1, 173-178 (1981) · Zbl 0473.93042 |
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.
