Representing a nonlinear state space system as a set of higher-order differential equations in the inputs and outputs
The paper is concerned with the problem of transforming a smooth nonlinear control system with outputs in the state space representation into an equivalent input-output (external) representation. The problem recently has attracted considerable attention within the differential algebraic approach in control theory. In this paper a strict algorithm is presented which realizes the transformation locally, provided that certain rank conditions are satisfied. As the result the dynamics of the initial system are restricted to an unobservable part of state variables, while the remaining state variables are expressed in terms of jets of input and output functions, and the external behaviour of the system is found. The approach assumed in the paper resembles in the spirit that of \textit{Chun-Wen Li} and \textit{Yuan-Kun Feng} [Int. J. Control 45, 1147-1160 (1987; Zbl 0622.93028)].
scientific article; zbMATH DE number 4097197
scientific article