The Minimal Time-Varying Realization of a Nonlinear Time-Invariant System
Résumé
The state realization is called minimal if it is either accessible and observable or its state dimension is minimal. In the linear case those two de nitions are equivalent, but not for nonlinear time-invariant systems. It is shown that de nitions remain equivalent in case one is searching for minimal realization in a larger class of nonlinear time-varying systems.
First, nonlinear realization theory is recasted for time-varying nonlinear systems. A necessary and sufficient realizability condition is given in terms of integrability of certain subspace. The mathematical tools used for this purpose are the algebraic approach of di erential forms and the theory of the skew polynomial rings; these tools are again extended from time-invariant to time-varying systems.