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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\textit{A. V. Evseev} and \textit{V. N. Chetverikov}, Differ. Equ. 49, No. 12, 1609--1618 (2013; Zbl 1290.93042); translation from Differ. Uravn. 49, No. 12, 1654--1663 (2013)

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##### References:

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