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Simplification of the generalized state equations. (English) Zbl 1249.93094
Summary: The paper studies the problem of lowering the orders of input derivatives in nonlinear generalized state equations via generalized coordinate transformation. An alternative, computation-oriented proof is presented for the theorem, originally proved by Delaleau and Respondek, giving necessary and sufficient conditions for the existence of such a transformation, in terms of commutativity of certain vector fields. Moreover, the dual conditions in terms of 1-forms have been derived, allowing to calculate the new generalized state coordinates in a simpler way. The result is illustrated with an example, originally given by E. Delaleau and W. Respondek [J. Math. Syst. Estim. Control 5, No. 3, 375–378 (1995; Zbl 0852.93016)] but solved in an alternative way.
93C10 Nonlinear systems in control theory
93B27 Geometric methods
93B17 Transformations
93B11 System structure simplification
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