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Realizations and minimal realizations of input-output mappings of general form. (English. Russian original) Zbl 1290.93042
Differ. Equ. 49, No. 12, 1609-1618 (2013); translation from Differ. Uravn. 49, No. 12, 1654-1663 (2013).
Summary: We consider the problem of passage from the description of a nonlinear control system by a system of equations for the input-output mapping to a system of equations for the state variables. We solve the problems of such a passage with reducing the order of derivatives of the control and with reducing the order of the system of equations by eliminating the first integrals. The case in which the state equations do not include derivatives of the control was considered earlier; here we consider the general case. We obtain necessary and sufficient conditions for the existence and present algorithms for the construction of realizations and minimal realizations.
MSC:
93B15 Realizations from input-output data
93B40 Computational methods in systems theory (MSC2010)
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[1] Conte, G., Moog, C.H., and Perdon, A.M., Algebraic Methods for Nonlinear Control Systems, London, 2007. · Zbl 1130.93030
[2] Krishchenko, AP; Chetverikov, VN, Transformations of descriptions of nonlinear systems, Differ. Uravn., 45, 706-715, (2009)
[3] Krishchenko, AP; Chetverikov, VN, Minimal realizations of nonlinear systems, Differ. Uravn., 46, 1612-1622, (2010) · Zbl 1215.93031
[4] Delaleau, E; Respondek, W, Lowering the orders of derivatives of controls in generalized state space systems, J. Math. Syst. Estimat. Control, 5, 1-27, (1995) · Zbl 0852.93016
[5] Evseev, AV, Modification of the algorithm of the construction of a realization of the input-output mapping, (2011)
[6] Hunt, LR; Su, R; Meyer, G, Global transformations of nonlinear systems, IEEE Trans. Automat. Control, 28, 24-31, (1983) · Zbl 0502.93036
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